Squad numbers are submitted to the PL before the start of the season, but the club don’t officially announce the numbers until after the window closes, they always warn us not to purchase kit with players name and numbers until after the window closes. However as PL rules state a player can only use one number per season anyone named in our first match day squad will have that number for the season if you are looking to purchase kit.
Most players will have the numbers they’ve been pictured having on the front of training kit, but occasionally things can change (Alzate had something like number 46 in pre season last year, then wore the 17 shirt when the squad numbers were submitted).
Obviously changes are allowed so a player signed after the list is first submitted to the PL can be assigned a free number and a number can be reused if a player is sold/loaned out (Andone and Mac Allister both used the number 10 in the 19/20 season).