What kind of profitable business you can create with only $10K USD?

Lawn care business or cleaning business are the first ones that come to mind. Both have a relatively low barrier of entry. I was able to create a lawn care business for under $10k in upfront investment, and that means absolutely everything: marketing, website, pickup truck, covered trailer, mower, all misc tools. I did everything myself. Cleaning business has far less upfront cost and doesn't require as much hot outdoors work.

I've heard Dave Ramsey refer to coin car wash lots as a license to print money, but he also said he doesn't own any b/c it's not what he wants to get into. I never did research that claim, and I don't know how much money it would require but I'm guessing more than 10k.

One trick with this is to try to do it with as close to $0 as possible. Many apps fall into this category. Use the money for experiments, or to speed up things like data entry. Maybe for marketing or setting up a domain name.

And by trying to stick to $0, you tend to spot clever low cost marketing strategies that might actually be far more effective than putting $1000 on a Facebook ad. And you end up focusing on trying to get users right now rather than think in terms of runway, assets, and bloated features.

For example, we'd print out recipes and put them on some banners downtown, with link to our app for more.

Or we'd set up a fake blog and subscribe a domain name, with a single article that said "If You Are (target market), Here Are 5 Reasons You Must Download This App." It's shady but it brought in 3000 active users, who stuck around and shared it to their friends. The cost for that was around $100, including hiring a copywriter.

If you don't like apps, there's always something like dropshipping - be a middle man for two parties and make money off the arbitrage (which ironically scales well into an app). Some friends make a good sum collecting money for babysitters. One friend did a car rental business, but he got the cash up front first, then bought the car. Try to make it cost $0 where possible.

First, I will suggest reading $100 startup.

What skills do you have? Based on your skills, find low hanging fruits and go for them. No need to think too much or do any validation etc. Take a shotgun approach. Launch bunch of small projects and see what sticks.

Can you do WordPress? Can you learn quickly? Join affiliate programs and launch bunch of sites in obscure topics you know and/or interested in. Outsource writing to Fiverr, Upwork etc freelance sites.

a tiling business, assuming you like working with your hands and care about doing things well

Sell coronavirus masks

sneaker reselling

Prostitution? Drugs?

Oh, I'm guessing you mean legally. Didn't see that in the requirement specs though.