Attend your child's games as often as you can. Cheer for all the kids on the team. Help with fund raising. Assist with logistics. If you're not sure how to help, ask the coach.
Some organizations have a fairly well organized booster club that always needs volunteer help.
There is probably a hundred ways to be a good team member and a good parent at the same time. When the larger definition of team is working well, the experience can be wonderful for everyone involved. People who see your program in action will want to be a part of it. Parents looking ahead to when their child will be old enough to participate will want to fit in and help. This kind of teamwork perpetuates itself.