I'm making puzzles for a game and found out that you can find out what the night sky would have looked like on any particular date, is there any web site or app that can read a star map and tell someone the date from reading where the stars are on the map?
Not an "easy" way.
The stars don't move relative to each other enough to make their relative positions useful for finding the date. And the absolute positions of the stars repeat each year, and each night, so the position of the stars will be the same at 10pm on Dec 1st 2023 as on Dec 1st 2022, and the same as Nov 1st at 12am.
If there are planets or the moon on the map, you may have better luck. You could search through an almanac, or more conveniently get a planetarium software to search for you, for the dates on which the planet appeared at a given position. With three or four planets visible you should be able to get a good date. But there is no guarantee that there will be many planets above the horizon.
I know of no app that can read a star map, and find the date on which it was produced. The process of reading the map would be an application of artificial intelligence, so not a trivial matter.