What happens to the battery if I leave a newly bought iPhone SE unpacked for a long time?

It’s usually recommended for long term storage that a battery be stored in the middle of the charge range. Most Apple devices and replacement batteries are distributed this way. There’s nothing particularly damaging about charging up to 100%, turning it off, and leaving it in storage, but in the middle is supposed to be a little bit better for long term reliability.

Eventually it’s going to reach a deep discharge state (well below the 0% level that results in a forced auto shutdown), but that can take I’d think at least a year, and not likely if it started off at at least 50%. Deep discharge is more likely if it started off at close to 0% and is stored.

You might try just charging it to see what level it’s at. You wouldn’t need to activate it. It doesn’t need to be at a precise charge level for storage.

Why don't you return it for a refund and buy another one when you are closer to seeing your son?