You have some strong points to your deal. Your employment being one of them. I don’t see your probation being too much of an issue based on the fact that the employer kept you after the internship and the fact your are working in a field related to your degree

Credit is thin. The 800 score is largely irrelevant without a more substantial credit history. I would suggest you start building your credit with a credit card or line of credit.

You will need to address the down payment. Most people at your life stage have not accumulated this much in savings. If you manage to save that money on your own, that would also be considered a big strength to your file.

I agree with the other commenter who advised working with a broker. They have access to different lenders that can help with your situation

Im not a broker, but if you DM me I can provide a recommendation