You will encounter 3 checks on an internal USA flight:
- TSA gun/bomb/ "you have a ticket"* check.
- Boarding pass check by gate agent.
- Uber driver at destination checking that you are you.
The several States which united to form the USA already agreed on freedom of movement and commerce, so they also agreed on a sort of "super Schengen area" among them. The states entirely defer immigration to the Federal government, and take no role in immigration. Since the USA is also a trade union, there are no customs controls either, except for very minimal health inspections, e.g. California will not allow some seeds, animals and foods, to stop infestations nd invasive species. (Some nitwit seeded a Sierra reservoir with Northern Pike; had that reservoir spilled before this was discovered, it would have wiped out California salmon.)
So, the facilities simply don't exist to check and stamp your passport. There's not a "line" for that in airport layouts.
You will enter via TSA security (gun/knife/bomb check) into the domestic "sterile area" (sterile of guns, knives and bombs) intended for departures, with the wide selection of overpriced restaurants and shops. When your flight lands, you will exit the plane into that exact same domestic sterile area intended for departures. Feel free to stay inside the sterile area for a bit and overpay at a restaurant or shop :)
Notice how that differs from an international arrival, where you are pushed into an austere area with little but immigration.
You exit the sterile area, typically toward baggage claim. It will be a hallway that has a TSA agent posted, but their only job is to make sure nobody tries to enter the sterile area that way. They will ignore you. Their job could be replaced by a mechanical gate/turnstile, but that would confuse travelers and create a jam-up.
Once you go down that hallway, that's it. Welcome to New York, enjoy your stay.
* As such, they check your ID, but mainly to assure the ticket you have is yours. In the 80s, TSA didn't care if you had a ticket. In exploring cities with good public transit to their airport, I would often enter the sterile area and enjoy some of the more exotic restaurants there. I hope we are able to return to that someday.