I've been using Google Cloud Run for one of my hobby projects and it worked like a charm. You can have a Google Cloud Build job that takes your GitHub repo from which it builds a Docker image. You make sure that the CMD in the container starts your server. When a request comes in the container is started within ms. You only pay for the storage for the image & the cost from actually executing the container. If you get no requests, it's practically free which is important for my side projects, since there is hardly any traffic.

I tried to get a similar solution with AWS Lambda and API Gateway and it was a huge PITA in comparison.