I like to mention the 1875 french operetta "Le voyage dans la lune" (The journey to the moon, or From earth to moon) by Jacques Offenbach, basing loose at the book by Jules Verne.

The Boston Public Library wrote about it:

The opera ran for six months in Paris, opening in October of 1875 and closing in April 1876. It opened in Vienna and London in 1876. A review of a London performance describes the music as “thoroughly Offenbachian – that is to say, that it has melody, brightness, and ‘go,’ and that it is not altogether free from commonplace. Dullness, however, is a word unknown in M. Offenbach’s vocabulary; and hence the present production is as pleasing and animating as any of the works we are wont to associate with his name.”

A prince like to travel to the moon. He uses a cannon to fly inside the big bullet to the moon. There he falls in love with a princess.

It is not one hit, but was very popular in its time. There is no ranking possible here, because even radio was not a daily medium in this time.

This may (also) be a controversial answer. It's hard for me to address the popularity of this song in the context of a country, such as the United States, because it's not meant for that demographic.

This song is a Latter-day Saint hymn, first published in 1842. Among the LDS, the song is incredibly well know. I'm sure the 6 million+ LDS living in the US alone have all heard the song, or will here this song, many times in their life. That's a population greater than all but the top 110 or so countries, and that's without including international LDS members. There are also over 9000 (yes, seriously!) covers of this song on YouTube (and that's after removing the Mormon Tabernacle Choir).

The song is titled If You Could Hie to Kolob. While it is a religious piece, it has some very science-fiction-like elements when pondering the universe:

1. If you could hie to Kolob
   In the twinkling of an eye,
   And then continue onward
   With that same speed to fly,
   Do you think that you could ever,
   Through all eternity,
   Find out the generation
   Where Gods began to be?
2. Or see the grand beginning,
   Where space did not extend?
   Or view the last creation,
   Where Gods and matter end?
   Methinks the Spirit whispers,
   "No man has found 'pure space,'
   Nor seen the outside curtains,
   Where nothing has a place."
3. The works of God continue,
   And worlds and lives abound;
   Improvement and progression
   Have one eternal round.
   There is no end to matter;
   There is no end to space;
   There is no end to spirit;
   There is no end to race.

It has lyrics about being instantly transported to a distant planet named Kolob. Note that Kolob is the inspiration for Kobol in Battlestar Galactica.

Then, the lyrics are about flying through space, throughout eternity, to see the beginning and end of the universe. It also addresses a continuum of space and time.

Disclaimer: I don't mean to offend anyone by suggesting this religious piece, as I'm not calling the religion fiction. Just as Orson Scott Card and Brandon Sanderson have used their Sci-Fi and Fantasy to do so in their novels, I've always found these lyrics to be very Sci-Fi, as a way to ponder the ways and mysteries of the their god.

I would like to point out that I suggested this in appreciation of a song I've always enjoyed.

Allow me to be a little loose with the definition of "sci-fi" and I'll give you Santa Claus Is Coming To Town, first premiering in 1934.

It became an instant hit with orders for 100,000 copies of sheet music and more than 30,000 records sold within 24 hours.

While it was a bit too early in pop music history to have accurate numbers on popularity, at least one cover of the song, by The Four Seasons, made it to #23 on the Billboard charts.

This answer, of course, depends on whether or not you consider Santa Claus to by supernatural sci-fi, or supernatural fantasy. But the lyrics "sees you when you're sleeping" and "knows when you're awake" seem like clairvoyant powers, to me!

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If you like Santa Claus songs, there's also "Up on the Housetop" by Benjamin Hanby, written in 1864. The song is one of the oldest about Santa Claus. It's been popular and famous since its inception, and some of the covers have been incredibly famous. Kimberly Locke's 2005 version:

broke a Billboard record when it made the largest leap into the Top 5 in the AC chart's history, moving from 32 to 5 in only a week. It was also the second longest Billboard holiday AC chart topper in the chart's history, sitting at #1 for 4 consecutive weeks.

The notable sci-fi element in this song is the reference to the flying reindeer with "Up on the house top reindeers paused," aside from the modern Santa Claus reference in general.

TL;DR: I can think of two early Science Fiction songs - one made the Hot 100 charts; the other predates the Hot 100 charts, but was recorded by one of the most successful musicians of the early 20th century. Purple People Eater by Sheb Wooley, and Two Little Men in a Flying Saucer by Ella Fitzgerald.

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Purple People Eater by Sheb Wooley

This one definitely meets all your criteria.

No. 1 in the Billboard pop charts in 1958 from June 9 to July 14, and reached no. 12 overall.

You're not going to find an earlier sci-fi song that made the Billboard Hot 100 charts, because this song was released the same year that the Billboard Hot 100 charts began.¹

The song is about a man-eating alien who comes to earth to join a rock band.

Well I saw the thing comin' out of the sky
It had the one long horn, one big eye
I commenced to shakin' and I said "ooh-eee"
It looks like a purple eater to me

It was a one-eyed, one-horned, flyin' purple people eater
(One-eyed, one-horned, flyin' purple people eater)
A one-eyed, one-horned, flyin' purple people eater
Sure looks strange to me (One eye?)

Well he came down to earth and he lit in a tree
I said Mr. Purple People Eater, don't eat me
I heard him say in a voice so gruff
"I wouldn't eat you cuz you're so tough"

It was a one-eyed, one-horned, flyin' purple people eater
One-eyed, one-horned flyin' purple people eater
One-eyed, one-horned, flyin' purple people eater
Sure looks strange to me (One horn?)

I said Mr. Purple People Eater, what's your line
He said "It's eatin' purple people and it sure is fine
But that's not the reason that I came to land
I wanna get a job in a rock and roll band"

Well bless my soul, rock and roll, flyin' purple people eater
Pigeon-toed, undergrowed, flyin' purple people eater
(We wear short shorts)
Flyin' purple people eater
Sure looks strange to me

And then he swung from the tree and he lit on the ground
He started to rock, really rockin' around
It was a crazy ditty with a swingin' tune
Sing "a boop boop aboopa lopa lum bam boom"

Well bless my soul, rock and roll, flyin' purple people eater
Pigeon-toed, undergrowed, flyin' purple people eater
(I like short shorts)
Flyin' little people eater
Sure looks strange to me (Purple People?)

And then he went on his way, and then what do ya know
I saw him last night on a TV show
He was blowing it out, a'really knockin' em dead
Playin' rock and roll music through the horn in his head

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Two Little Men in a Flying Saucer by Ella Fitzgerald

Released in 1951, this single didn't hit the Billboard Hot 100 charts because the Billboard Hot 100 charts weren't invented until 1958. However, Fitzgerald had been one of the most popular musicians in the world for decades by the time she released this song, so it is worth mentioning.

The song is about two aliens who visit earth, decide humans are psychotic morons, and quickly leave.

Two little men in a flying saucer
flew down to Earth one day
Looked to left and right of it,
couldn’t stand the sight of it
and said let’s fly away

They took a look at a Western movie,
somebody heard them say
If a horse can be a star,
think how dumb the people are
We’d better fly away

Then they shook their little green antennas,
scratched their purple hair
Said this planet is an awful menace,
let’s go back to where
we came from

Two little men in a flying saucer
just didn’t care to stay
Said it’s too peculiar here,
headed for the stratosphere
and quickly flew away

Now they took a left in Ebbet's Field in Brooklyn
when the Dodgers played a baseball game
Heard all the screaming,
said we must be dreaming
‘cause this planet is insane

During intermission,
heard a politician
making speeches as they traveled by
But they departed
faster than they started
‘cause the holler blew them sky high

Two little men in a flying saucer
flew down to Earth one day
Listened to a radio,
saw a television show
and said let’s fly away

They got their fill of commercial jingles
and they were heard to say
All the people seem to be living in a nursery
we’d better fly away

Traveled all around and once they’d seen us
said let’s head for space
We were better off on Mars and Venus,
goodness what a place to live in

Two little men in a flying saucer
just didn’t care to stay
Crossed a crowded thoroughfare,
saw the hats the women wear
and quickly flew away
And quickly flew away

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Honorable mention:

Thirteen Women (and Only One Man In Town), Bill Haley and His Comets - 1952/1955²

Mr. Spaceman, The Byrds - 1966

In the Year 2525, Zager and Evans - 1969

A Space Oddity, David Bowie - 1969

The Rise and Fall of Ziggy Stardust and the Spiders From Mars (album), David Bowie - 1972

It Came Out of the Sky, Creedence Clearwater Revival - 1969

2000 Light Years From Home, The Rolling Stones - 1967

Big Yellow Taxi, Joni Mitchell - 1970

A Hard Rain's A-Gonna Fall, Bob Dylan - 1963

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¹Prior to 1958, Billboard had charts of popular songs (beginning in 1941), but they were limited to the bestselling song of each week; because songs tended to be bestsellers for many weeks, the charts for a year might include as few as 3 songs.

I looked through the bestsellers lists from 1941 to 1957, and there are no songs that clearly fit the sci-fi criteria. The ones that come closest are as follows:

The Gypsy, The Ink Spots - 1946

(Ghost) Riders in the Sky: A Cowboy Legend, Vaughn Monroe and his Orchestra - 1949

Swinging on a Star, Perry Como - 1944

Mr. Sandman, The Chordettes - 1954

Rudolph the Red-Nosed Reindeer, Gene Autry - 1950

²B-Side to the hit Rock Around the Clock; credit to user14111 for the suggestion. The single Rock Around the Clock/Thirteen Women was released in 1952 with the latter track as the A-Side; it didn't do very well. When the song Rock Around the Clock was used in the 1955 film Blackboard Jungle, the single was re-released with Thirteen Women as the B-Side, and topped the charts.