Short sweet straight to the point:
https://tennispredict.com/tennis-levels/#:~:text=6.0-7.0%20%E2%80%93%20Pro%20player%20%28Top%201000%20ATP%20or,5.5%20%3D%20Advanced%206.0%20%E2%80%93%207.0%20%3D%20Professional
How players start off
As far as my understanding goes, tennis players are only considered full professionals once they play an ATP match. To get here though, most players start entering junior and childrens tennis tournaments at a young age to get practice being around crowds, learning fundamental rules, getting used to different circumstances and environments .etc. Winning matches here increase their ranking and points. If you'd be interested the USTA site has tournament information available for the US.
ITFs to ATPs
Once players think they're ready, they can then advance to a Futures/ITF tournament, which is an important stepping stone to getting to ATP tournaments. A player who wins one of these tournaments can earn up to 35 points in the ATP ranking system.
In response to your initial question, yes players are technically professionals once here, but the reason why most climb up to around 1000 before going fully professional and entering ATP tournaments is because it's simply a comfortable place to be in the beginning of an ATP career. By this I mean the player knows they have lots of experience and is usually more confident in their abilities at this time, plus they wouldn't have to spend as much time in the lower rankings of ATP, but if course that also depends on their skill.
It's important to know that there are no minimum ranking requirements to enter a ATP tournament, yet the 1000ish ranking is pretty normalized for when players would decide to enter one. I'm pretty sure you can simply go to the ATP website and sign up for one. The answer of this question: Qualifying criteria to an ATP tournament.
explains this specifically from the ATP Regulations, but I'd suggest you go to the actual site for more clarity and anything I missed or didn't explain well.
This was a bit long winded but I hope it helped at least a bit.