While it is possible to put the SHA-256 algorithm into an FPGA, in general it isn't cost effective to do so if you are seeking a profit on your effort. Back in the 2012-2013 time frame, there were multiple FPGA efforts for Bitcoin mining. At the time they were a step forward, but have been completely replaced by ASIC in terms of profit seekers since the end of 2013.

While I think it's a dandy home project, you should plan on getting your satisfaction from making it work at all.