You have 60 days from date of purchase of the iPhone to get Apple Care+.
After that, you cannot get Apple Care+.
And if you were to break the screen during those 60 days you would not be able to get Apple Care+ either.
Apple Care+ needs to be bought while the iPhone is in perfect working order, less than 60 days old.
The screen repair cost for an iPhone X is $279 U.S. Price may change if you are somewhere other than the U.S.