My son is 2 years old dec 25 born .. for the same socialize reason , we have signed him for my little gym . His batch is 2-3 years old. This is his 4th month in the gym and he is very socialize with other kids now .
If he's not a "big for his age" kid, I wouldn't. Find a 2's class and look for a mom's group so he can see the same kids regularly.
Gymnastics it’s a good choice. I wouldn’t sign him up for 3-4 years old class unless he is very outgoing and bigger than others. 3-4 years old kids are very explosive and sort of out of control. They are naturally not very considerate about other kids so your boy most probably would get left behind or hurt by them. I signed up my daughter for soccer with older kids and it didn’t work out. Now she does gymnastics, swimming activities at the local library and just going to various playgrounds
See if you have a KidStrong or My Gym in your area.
I wouldn't be concerned about size if his interest and attention is there!
At 2 we signed our little guy up for parent and tot activities like gymnastics (he loved it!)
I tried a sport at 4 and that felt too early for me, it was rough to watch my son as he was the youngest on the team and didn’t have the attention span for it .
I signed my 2 yr old up for soccer and it didn’t work out. I got refunded. I wanted to socialize him and run his energy out I’m hoping maybe in the Fall it will work out better at 2 1/2. Good luck! 🍀