App Engine custom domain with service

Check how to use subdomains and how wildcard mapping works in the GCP docs here (actually these are the next steps at the website which you've followed and linked). Make sure that your DNS provider permits wildcards in CNAME host entries, otherwise such mapping will not be possible.

This blog post shows a real-life example of matching subdomains to services with App Engine.

Here's a step-by-step:

1. Ensure you are a owner of the parent domain in here: https://www.google.com/webmasters/verification/home (e.g for subdomain.example.com you need to own example.com) If not, ask a friend to add you as an owner.
2. Create a CNAME record pointing to: ghs.googlehosted.com (in Cloud DNS or wherever). Note: This will cause downtime, but it is required for App Engine to create an SSL certificate so downtime is unavoidable...
3. Add custom domain to App Engine
   1. Go to App Engine -> Settings -> Custom Domains
   2. Click on Add a custom domain
   3. Choose the verified parent domain and click Continue
   4. Enter the subdomain (e.g subdomain.example.com) and click Save mappings
   5. Click Done (you already did this last step)
4. Update App Engine dispatch rules
   1. Run gcloud app describe --project <GOOGLE_CLOUD_PROJECT_ID> and take a look at the current section of dispatchRules
   2. Create dispatch.yaml or dispatch.yml file with your new rule as well as the ones already existing above (note the file format is different from the command output)

   dispatch:
     - url: <DOMAIN>/* # e.g. subdomain.example.com/*
       service: <SERVICE-NAME>
   

   3. Deploy it using: gcloud app deploy dispatch.yaml --project <GOOGLE_CLOUD_PROJECT_ID>