can a disabled couple on SSD get a mortgage?

Hello, married disabled couple ages 41 and 43 looking to be first time home owners. Credit score is fair(though I don’t know why, was able to get a new car loan and credit card and they have been paid on time for 6 months) have 2 delinquent loans of total $ 1500 that will be paid off in the next month(hope that raises the score) Home in NY will be around $ 200,000. Down payment will be $ 40,000(thanks in part to my mother). Score is 569. I am expecting to pay around 7% interest(I based that on our score but the lower the better). Income is $ 3700(no taxes are taken out of SSD and disabiltiy insurance) a month and the mortgage calculators I’ve used said we can get a $ 162,000 loan. Can this happen? Should I keep dreaming? I am trying to be realistic. Based on anyones experience with what I have written is this feasable? I know a mortgage specialist will help us but I wanted to ask here first. Thank you!

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