@Danny Mittler I'll come at this from a different angle since BRRRR might be different than what you're thinking it is. The idea isn't to get an FHA loan to house hack, it's to find an off-market property that you can rehab and then rent out to a long-term tenant or use as a STR on the backend (highly recommend the latter). An FHA loan isn't going to help you, hard money or private lenders will help you finance a BRRRR property.
With $30k saved, you're probably looking at a purchase price around $120-150k max. Certainly possible in cheaper markets like Florida, just might take some digging to find. A local contractor is going to help you with the rehab, but if this is your first project I would recommend partnering with someone who has done fix n flips before so you don't get caught off guard.
Once the project is complete, you need to find a lender who will do a cash-out refinance for the property. As long as you qualify (I don't know enough about your background to say either way), the goal is to find a lender who will lend at least 75% of the ARV as a cash-out refi. Some lenders have seasoning requirements (meaning you have to rent it out for a certain amount of time), other lenders like Better.com could care less.
It is a myth to think you'll get all of your cash back in a refi, but even if you have some cash left over after paying back the hard money/private lender that's still a win. If the market supports it, again I'd recommend doing a short-term rental to achieve a higher cash-on-cash return. Otherwise if you want more stability and less headaches, find a long-term tenant that can cover your loan payments.
Good luck and hope you land that first BRRRR!