Since you are hosting a Static web page, you could take a different approach and host it on Cloud Storage, this is totally supported by google. You can follow this tutorial.
If you want to host it on App engine, check the type of instance you have configured, it maybe too small, you could try a bigger instance type, and also check if you have auto scale enable, maybe you are running out of resources, which the compute engine instance did provide. Also take a look to this GCP blog post and see if you can help you troubleshoot.
Also you could take a look into you .yaml file, and make use of “options default_expiration” or the “expiration” elements. More info here
If you're App engine is a standard environment you can server files from another GCP product or from CDN. Here is some info.
All the code related docs are on python but you can change it yo many other runtimes in the top right corner of the page
Hope it's usefull.