Q: How do you even speedrun rocket league?
A: There is a season mode in the game against AI opponents, which can act as this game's "story mode" in a sense. There is, after all, an ending and credits.

Q: Okay.. but every match has a strict five minute time limit, how do you even save any time?
A: To save time in this game, you have to cut out as many replays and overtime battles as possible. Optimally, this means ending every match with a score of 1-0. You can even lose some matches 1-0, as long as you have enough wins to get to the championship game. Doing this for every single game is difficult, because you essentially have to stop 5 AI from scoring on EITHER goal. The more games you cause to have a 1-0 score, the faster your time will be. 2-0 scores aren't that bad either, but you want to avoid overtime at all costs. You can also save a little time each game by having fast kickoffs (timer doesn't start ticking down until the ball is hit), and by making sure the ball is on the ground when the timer is about to hit 0 (the game can't end with the ball in the air).

Q: So if teammates scoring is an issue, and this is a speedrun, why not just set season mode to 1 vs. 1 matches only and set it to be a shorter season?
A: Since there are MANY different potential categories and variants for season mode, it's simplest to make the "default" speedrun category use the default season mode rules in the game. Also, having to try to stop your own teammates from scoring makes the run more interesting.