Questions about 180 day tourist visa

I’ve been doing a lot of googling and searching through this sub but I’m still very confused about some things. I’m an American and interested in living in Mexico, at least for a few months to begin with to see if I like it. I would be working remotely during that time period doing online tutoring. I know Americans can stay for up to 180 days before having to leave the country, and that we can return for another possible 180 days, if so granted. Suppose after a year I decide that I love living in Mexico and want to establish residency. Do I then have to leave Mexico and apply for temporary residency from the US? Would the financial solvency requirements still apply, because those numbers are pretty steep.