Why not play 2x2? Or even 1x1? You can start any game by checking the ball like you do in 3x3, and from there you can time, and score, however you want. Lots of people play basketball in their own way, with their own rules that make sense for them, so why not give it a try yourself?
As a lot of basketball at 3x3, 2x2 and 1x1 is informal and just between friends for fun, you often won’t have a referee to call fouls. Its important players are safe, play within the rules and don’t do anything that might cause an injury. It’s always a good idea before you play to know the basic rules of the game so that when you do something that is a foul, you can let everyone know, check the ball and start again.
If you need to, you can even play basketball on your own! Try taking shots from different parts of the court, and if you make a shot, give yourself a point. If you miss, give that point to your imaginary opponent. See if you can make enough shots in a row to be the first to 10, 15, 21 or whatever number you want to play up to. Basketball really is a sport for everyone, no matter what.