I have transported my surfboard in my Model 3 by letting it stick out of the trunk, fin down. Worked reasonably well. The Model Y is a trace longer and wider, so it should be even easier to do that.
You have to tie down the trunk lid. I used two blankets, one to protect the seats and one wrapped around the board to protect the trunk opening and also the board from the lid lock.
There are a few tricks. One is to pull the tie-down belt into the trunk lid lock, so the lock closes, and it looks to the electronics as if the trunk is closed. If you don't, the car will complain about the open trunk for a minute when you drive off, but then it will stop. But using the trunk lid lock is almost the only way to tie down the lid, so try to do that.
I had the front passenger seat folded forward as far as possible to be able to push the board a bit further forward.
Warning: Check the traffic rules in your country about how far anything is permitted to stick out at the rear. I'm in Germany. The rules here are a bit strange. If something sticks out for more than 1 meter, it has to have a red flag at the end. For a distance of up to 100 kilometers something may stick out by 3 m; on longer drives only 1.5 m are permitted. I wonder how they check this. Anyway, rules can be peculiar. My board stuck out less than 1 m, so I was fine even without the red flag.
The partly open trunk can cause some problems. When you drive fast, it can be noisy, depending on how other things are arranged in the trunk. Things can be sucked out, so be careful there. Drive slowly. I tried speeds up to 120 km/h = 75 mph and had no problems, but didn't dare to go faster. Mostly I drove more slowly.
Anyway, I had pondered the thought of buying a roof rack, but have now decided against it. I may never need one.
