Hello, and thank you for writing. I wish I had better news for you. The USDA is also a government-backed loan, and it actually has a higher minimum credit score than FHA does (640 vs 580).
But it might not be your credit score holding you back. Owing child support arrearages (past-due amounts) is not always a reason in itself for being declined for a mortgage. However, if the government had to force you to repay past-due child support, government-backed mortgage problems can be off limits for a while.
That's because of a database called CAIVRS (pronounced "cavers") that tracks people who have defaulted on government-backed loans like college, small business or mortgage loans. Also taxes and child support obligations, in some cases. The agency reporting you to CAIVRS has to clear you. It may be willing to do so if you have been making your payments on time for a number of months or years.
Other reasons for child support causing loan denial is that judgments in court are major derogatory events that can bring your FICO score down. If a lender considers back child support the way it does other collection accounts, it will likely require payment in full or at least 12 months of on-time payments.
The good news is that once you make up the past-due amounts, you'll have a little more in your pocket each month, and you can put that toward other debts, a larger down payment, or emergency savings. Any of those things will make it easier to get a loan when you're ready. If your credit score is good and the only issue is the child support, a non-government backed loan may be easier to get right now than a government-backed home loan.