Where did the Alien Queen come from?

As far as I know, there is no officially canon answer for how the queen in Aliens got there. However, there are two ways a queen can come about - either from super/royal facehuggers (shown in the Director's Cut of Alien 3) or from molting (shown in the Alien vs. Predator (2010) video game).

Royal Facehuggers

In the Assembly Cut of Alien 3, it is shown that there are darker-colored facehuggers that have armor and spines whose embryo will eventually grow into a a queen. Presumably, these facehuggers hatched from eggs also laid by a queen, and can lay dormant the same way normal eggs can. It seems safe to assume that within the Space Jockey ship on LV426, there was an egg containing a royal facehugger, to hatch a new queen.

For reference, here is a picture of the prop used:

Molting

In the Alien vs. Predator (2010) video game, an alien grown by Dr. Groves named Specimen 6 actually goes through the process of molting, first into a Praetorian and then into a Queen. However, there is speculation that the Royal Jelly (produced by queens) held in containers that were destroyed by Specimen 6 throughout the game may have caused this transition. Given that the canonity of the game is questionable and there is speculation about the process, this is obviously secondary to the method above.

In the comic book Alien - Genocide, a colony of aliens bereft of their queen, bring up a new queen by themselves, using an existing egg. So all you need are aliens + egg that's not developed yet, to make a new queen. While the story do not state it explicitly, there's probably an intended analogue with bees, where worker bees can choose to bring up a new queen by feeding it extra food.

To further complicate the argument, during Alien: Covenant, David shows the Captain Elizabeth Shaws grave, and refers to her as "Mother", once while standing on the balcony where her headstone is placed, and again when Walter confronts him while playing the flute.

What can be derived from this, is for 10 years, while trapped on the engineers world, David, dissected and utilized Elizabeth Shaws reproductive organs, and hybridized human and Alien DNA, to there by create the first QUEEN. Owing homage to Elizabeth Shaw, as "MOTHER".

David also, stipulates that while waiting and experimenting on the Engineers world, his "successes", were merely waiting.. On "Mother", which can elude to the ending scene of Covenant, where Daniels and Tennessee are put into cyrostasis, for later use as hosts.

In my opinion, the eggs on the engineer home world had to be laid, so Shaw had to provide the necessary biological components, explaining why David killed, and dissected her. Thus creating the FIRST QUEEN.

It's said in one of the books (maybe Bishop in the Aliens novel) that in the absence of a queen, a drone is able to moult into a queen. I'd assume the drone would cocoon some humans in Hadley's Hope, moult, lay eggs, and then produce more drones.