Why doesn't my Google icon show on my home page on my iPad 10.2

Perhaps you have deleted just the Home Screen icon - as this is now possible in iPadOS15. Can you find the App in the App Library - now also a feature of iPadOS15?

See >>> Use the App Library and Home Screen to organize your iPad apps - Apple Support

More information:

https://www.idownloadblog.com/2021/12/02/how-to-unhide-apps-iphone-ipad-watch/

Apps are downloaded and installed from the Apple App Store.

The iPad User Guide is a rich (and often overlooked) source of information about using iPad and its many features. The Guide is available both online using a web browser (such as Safari), or as an Apple Books download:

iPad User Guide - Apple Support

https://books.apple.com/book/id1567104892

If the App icon is neither visible on a Home Screen, nor visible in the App Library, the App is not installed on your iPad.