Is there an idiom for saying something that might turn out wrong or making a wild prediction?

Perhaps you're looking for this: A shot in the dark

an attempt to guess something when you have no information or knowledge about the subject and therefore cannot possibly know what the answer is

[Cambridge]

You can use the expression:

A wild guess:

a guess based on no knowledge or information.

(M-W)

• It might be a wild guess, but Brasil will win this world cup.

The metaphor off the top of one's head can have this meaning:

(right) off the top of one's head

Fig. without giving it too much thought or without precise knowledge.

[McGraw-Hill Dictionary of American Idioms and Phrasal Verbs]

• I might be talking off the top of my head, but Brasil are going to win this World Cup.

The Free Dictionary by Farlex has this idiom:

go out on a limb

To do or say something that lacks evidence or support.

She really went out on a limb with that hypothesis—the facts don't support it at all.
That politician went out on a limb and publicly questioned the views of his party.
I don't think I'm going out on a limb by saying that everyone will like that idea.

Also

If you go out on a limb, you do something or say something that is different from what most people do or say and is therefore risky.