I have a 4 year old and a car seat that is probably as big as a royal throne. Before we had her in a rear facing one.The 3 has a very deep trunk. It just isn't as tall as the Y's hatch, but length is pretty much the same. One thing to note, they never compare the 3 and Y storage volume apples to apples. It is because the increase isn't as good as you might think.
An often overlooked aspect is the Y is Y'd open in the back. Get it Y'd (wide) open? So I got a lot more noise from the boom box hatchback aspect of it than the closed off trunk of the 3. While the Y has more headroom, the 3 has an inch more legroom. The Y's efficiency was worse even than my Model S's.
I am a big guy and far from my 20's, it isn't much worse for me to get in the 3 than my Y was. I may spend 5 seconds getting in or out but hours in the boring Y. I have to say it was the one car, in the past 2 decades, that I've had the most buyer's remorse after buying it. Not a day goes buy since selling it and getting the Y that I ever miss it to be honest. Even with knees that have seen better days from motorcycle racing and being a hockey goalie, I still can easily get in my 3.
I hate to say it but I'd buy a Kia EV6 over a Model Y in a heartbeat. Good luck with whatever you buy.