FHA loans require a minimum credit score of 500 for a loan with a LTV of under 90% and 580 for a loan with a downpayment under 10%. However, mortgage lenders generally require a minimum credit score of 620.
One important point you did not address is your DTI (debt to income ratio) and your overall financial situation. Mortgage lenders do use compensating factors. If for example you have a large investment portfolio, or a large stable income with no debt and your DTI is low, then you might find a mortgage lender who will offer a loan. You will have more chance of finding a local bank or credit union that holds on to the loan on their own portfolio (and don't sell the loan to Fannie Mae, Freddie Mac).
You asked about hard money lenders. The sub-prime market pretty much dried up after the 2007-2008 crash. If you do find private money lenders, then you will be looking at high interest rate, high cost loans. Those loans usually have terms that make the loans very risky, including balloon payments. In general, I would advise against these types of loans.
Your next step: Prepare your finances, check out your DTI level and then shop around with a local lender to get a feel for the market.