AWS Api gateway: How to expose new services automatically?

I'm searching for a way to expose service routes to Api Gateway automatically. The flow should be the following:

1. New service in EKS is created
2. Two proxy resources added to api gateway /public/{service-name} and /private/{service-name}
3. Integration with new service added to created resources (perhaps we would have ALB per service, so it resource integration would be done through ALB)
4. Api gateway redeployed

So far, I've come up with the solution using a lambda function which will listen to cloudtrail ALB creation event and make calls to API gateway to create new resources and publish them

but I feel that there should be something more AWS native that works out of the box.