When comparing Google App Engine’s performance with the local one you should keep in mind that deploying on GAE needs more time in order to import all the necessary libraries and set up the Django framework.
Here , it is stated that Instance Startup Time for Standard Environment is up to seconds and for Flexible up to minutes. Additionally, I found some StackOverflow posts that shed some light on this here and here.
You may profile your application by using Cloud Trace to analyze the requests and isolate what causes the issue so that you may improve it afterwards.
In addition to that there are various ways to optimize your application’s performance, as the following typical ones:
Scaling configuration, by setting up “min_idle_instances” to be kept running and ready to serve traffic.
using Warm Up Requests to reduce request and response latency during the time when your app's code is being loaded to a newly created instance.
Furthermore, here and here you may find the official Running Django on the App Engine environments tutorials so that you can spot any details you may have missed.
Finally, during my investigation, I came across PageSpeed Insights, which analyzes the content of a web page, then generates suggestions to make that page faster and could be handy.
I hope this information is helpful and point you in the right direction.