I did say "most" states. I used to work at a car dealer's service department, and I've seen some cars come in where they don't have a state inspection sticker because the owner just moved from a state that doesn't do state inspections.
Because of that job, I've also seen stickers from other states that do do state inspections. Most of them will be on the windshield either in the bottom corner on the driver's side or in the bottom center. They'll list a month and year as numbers (ex. 8 and 24 for August 2024) for when the inspection sticker expires.
So, at least in my state, someone with 8/24 on their sticker would at least need to drop their vehicle off at a mechanic (not necessarily the car dealer, just a mechanic authorized to do state inspections) by the last day of the month. If the mechanic doesn't do the inspection until the the beginning of the next month, that's fine. You'd just get a sticker that says 9/25 on it when they're done.