I know the struggle at the beggining of a game where you have to do some repetitive job that you don't want just to get the rank to get what you want.

One thing that i'd like to suggest is to have saying 20% of your lastest XP level as your begining of your next game. Capped at Caporal.

Saying you are Private +1000xp at the end of a game, for the next game, you would be Private +200xp.

If you were Major at the end of a game, you will be Caporal at the beggining of the next one.

This idea need thoughts about when the player leaves for a couple of games. Saying he plays 2h a day, it would be nice to keep a bit from one day to the next.
One way would be to have this bonus for 7days. This bonus is reset each time you play a game > 30min (to prevent reset when you load at the end of a game)