I think your son just needs more time to adjust to new situations. He seems like an introvert. When he first started going to pre-k, did he have a hard time adjusting? If so, then may be it's the same with outside activities. My daughter is the same. She's a shy person and takes awhile to adjust to new situations. Even when we go to familiar places (friends' houses, relatives' houses), it takes her a few minutes to get comfortable. She, too, is in soccer with her friends and is doing really well. When you see her on the field, you don't realize that she's a shy little girl because she's out there going after the ball. My husband and I are very impressed and proud of her. I think it helps that her friends are there, but I think she'd be fine if they missed a game. If we are in a situation where she's standoffish and to shy to interact, I'll try to reassure her that everything is fine and will gently push her to go out and play. If not, then I'll let her be and let her decide to play at her own pace. She eventually does. I think it's best not to push your son too much. I think you should help him try new things, but don't force him to do it because the experience won't be fun for either of you.
As for Kindergarten, I'm worried, too, about how she'll adjust, but I know in the end she'll do just fine. We are already talking to her about Kindergarten and letting her know that she won't see her pre-k friends because they're going to different schools, but that she'll meet new ones. I also let her know that we'll plan playdates with her pre-k friends once school starts so she won't miss them as much. I have no idea if this is helping, but we'll see. I also plan on taking a few days off from work, so that I can drop her off at school and pick her up. My father in law watches our youngest and will most likely be the one picking her up from school, but for the first few days I'll do it so she feels more at ease. I think there's also a Kindergarten Round-Up at the school in the next couple months, so that parents can meet the Kindergarten teachers. Hopefully, we can bring our daughter so she can meet them before school starts.
Hang in there and good luck!