Add a “vote to keep” button at the end of the match. If you voted for someone that votes for you, the 2 (or 4 or 8, it depends on how likeable you are) of you stay on the same team for the next match.
This way after 3 or 4 matches you will probably have a party of great teammates with who you like to play and they like to play with you.
The simplest way to start this going would be maybe when selecting a player in the scoreboard at the end of the match, press menu to keep (or add to fireteam works too, but im not sure if your fireteam chat can comunicate with the other teammates in game if they are not in it). It may sound silly but some players dont want to be the one inviting,
Secret vote would be easier for socially akward people before the invite to fireteam or friend request