Advice: how to handle a shy kid in social situations?

My 5yo is super shy. Clings to me at birthday parties, won't participate in activities, cries if we try to push him. I'm not forcing anything but I'm wondering if there's a better way to help him get comfortable? Or should I just let him go at his own pace? He starts kindergarten in the fall and I'm honestly a bit worried. How have other dads handled this?