I've been reading a lot about how to train your Parakeet, and I made the mistake of letting her out too early to fly I think...

I've had her for 3 day and I let her out by accident while cleaning her dishes with the door opened.

She hasn't been hand trained yet, and is full flight.

Long story short I finally got her back in her cage, but will she be able to trust me any time soon, and when should I let her out again?

Welcome!

There will always be mistakes along the way. This is a decade-plus-long pet, not one of a few months . A minor hiccup is no reason to give up!

Start from the beginning and take it a day at a time. You're building a foundation here, not winning a race .