[Vuejs]-How to deploy frontend application to GCE properly?

Firebase is the simplest way to deploy your frontend on Google’s infrastructure. It handles certificate provisioning for you, so you get HTTPS out of the box. I’m not sure why you think Cloud Functions is the only backend you can use with it. You can use any backend you like, including Amazon’s ElasticBeanstalk. I use both App Engine and Compute Engine backends with a Firebase frontend.

You could also do it the “old way” (how it was done when App Engine was Google’s only cloud offering), and deploy your frontend to App Engine; it handles static content just fine.

There’s not a single right way to do it. Your options are vast, and choosing one service to serve your frontend content in no way limits your choice for running your backend.