I know not everyone wants to hear it, but having a child requires sacrifice.
If it's more affordable/practical to have one parent stay at home with the child, while the other works, then that's what needs to be done. There's no shame with one parent watching their own kid while their partner works, then their partner can care for the child while the other goes to their job.
These are things that need to be planned and discussed BEFORE having a child. It's all part of the deal.
Sports have always been expensive, and prohibitive to the point of discriminating against low-income families. This is not a childcare issue, but an issue with how sports and services are being delivered. I went through the same with gymnastics for our daughter, and various activities for our son, so I completely understand how unfair that is.