I’m a member of a couple organizations that became non-profits 501 ( c ) 3. One took 20 months and almost $2500 for filings, lawyers, CPA and documents. The other had a grant writer that also set-up non-profits as her business, she did it free for us. That on took 2 years.
I think you might be putting the cart before the horse there. It’s going to be difficult to run any kind of business, even/especially a 501( c), when you’re homeless. Get your life together, get yourself rooted and established somewhere for awhile, then perhaps you can see about starting a non-profit.