$10k to start REI business- Fact or Fiction

So, I've heard from many sources that you need $10,000 minimum to start investing in REI (for down payments, etc). I HAD saved $10k and was ready to start my BRRRR strategy remotely in Cleveland from California but our first born came a month early on April 1st. Due to an emergency c-section, the wife can't work for two months and she dipped into my funds to pay bills and we can't pay it back. So that leaves me with $6k to start investing. My question is is this do-able? Is the 10k minimum fact or fiction?

I'm trying to ask myself "How can I make this work". :)