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For a cash-out refi on a home the borrower lives in, generally, the lowest credit score is 640, according to Fannie Mae's standards. But such a loan comes with caveats. The borrower can't have an LTV ratio higher than 75%, must have 6 months of reserves in the bank and a debt-to-income ratio of 36% or lower.
(75 reviews). Different lenders have different guidelines but in general, you will have to wait 6 months to refinance into a conforming Fannie / Freddie loan. I do not think you will be able to recoup your $10K post purchase investment. I think you will just be able to refi up to your mortgage amount which in this case is below 80%- A good thing.