I am looking for an idiom or phrase used in informal speech that means "we're doing something without having all the necessary information" or something alone that line. Is there any such idiom?
There's flying blind, which means to do something by guesswork or intuition, without help. Link It can also express that someone is unsure of their course of action, but proceeding anyhow.
A: "What are you doing?"
B: "I don't know, I'm flying blind here!"
Not sure if this is exactly what you're looking for, but I have a couple that may be helpful:
Biting off more than one can chew
This means you are trying to do too much, more than you can handle.
To [try to] boil the ocean
This also means you are trying to do too much, and it also has a connotation that you are trying to do something that there's no point in doing.
These don't really mean exactly what you said, but they are similar, and even with research I can't find one that necessarily means exactly what you said. Hope it helped anyway!