Unfortunately, not having the 2 years of steady income will be an issue. Most lenders want a credit score of 620 (or better) with a steady 2 year income history. Although, there are some lenders out there that will attempt to work with someone in the upper 500's, where you are. It's not having 2 years of income that I think may be your downfall. But it never hurts to shop lenders to see if anyone is willing to take a chance on you. Once you have a full time job, along with your part-time work history, check with lenders again.