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Lots of people have had good success, I was able to get a new car right after discharge from Toyota. Check out the Cap 1 autoloans, I hear lots get approved right after BK.
What are your score looking like? Have you started the rebuilding process yet?
Carvana may give you a prequal approval as soon as your discharge is reporting, and you can see what that would be without taking a hard pull.
If you were discharged yesterday, it may not be showing on your credit report yet. Once it's reporting correctly, that should help with all of them.
It depends, could be fast or not happen. I had to disbute the CRAs to get it corrected, took weeks.
I purchased a new 2018 Chevy Trax two days post BK discharge, and got 9.9% rate, approved by GM. (for a used one it was going to be a lot higher APR, I was VERY happy). My score was in the 550's at the time. So it can be done! I called right into the finance division of the dealership and talked, told them my issue. They worked and worked with me, and I couldn't be happier. Just wanted to let you know it IS possible. Best of luck to you.
There's also a great auto forum on here that may be helpful to you.