GKE Ingress: https://cloud.google.com/kubernetes-engine/docs/concepts/ingress
Nginx Ingress: https://kubernetes.github.io/ingress-nginx/
Why GKE Ingress
GKE Ingress can be used along with Google's managed SSL certificates. These certificates are deployed in edge servers of load balancer which results in very low TTFB (time to first byte)
What's wrong about GKE Ingress
The HTTP/domain routing is done in the load balancer using 'forward rules' which is very pricy. Costs around $7.2 per rule. Each domain requires one rule.
Why Nginx Ingress
Nginx Ingress also creates (TCP/UP) load balancer where we can specify routing of HTTP/domain using ingress controller. Since the routing is done inside the cluster there are no additional costs on adding domains into the rules
What's wrong about Nginx Ingress
To enable SSL, we can use cert-manager. But as I mentioned above, Google's managed certificate deploy certificates in edge servers which results in very low latency
My Question
Is it possible to use both of them together? So that HTTPS requests first hit GKE ingress which will terminate SSL and route the traffic to Nginx ingress which will route it to corresponding pods
Is not possible to point an Ingress to another Ingress. Furthermore and in your particular case, is also not possible to point a GCE ingress class to Nginx since it relies in an HTTP(S) Load Balancer, which can only have GCE instances/instances groups (basically the node pools in GKE), or GCS buckets as backends.
If you were to deploy an Nginx ingress using GKE, it will spin up a Network Load Balancer which is not a valid backend for the HTTP(S) Load Balancer.
So is neither possible via Ingress nor GCP infrastructure features. However, if you need the GCE ingress class to be hit first, and then, manage further routing with Nginx, you might want to consider having Nginx as a Kubernetes Service/Deployment to manage the incoming traffic once is within the cluster network.
You can create a ClusterIP service for internally accessing your Nginx deployment and from there, using cluster-local hostnames to redirect to other services/applications within the cluster.