It's now been a couple of weeks since I started adding Structured Data to this site and Google has started to index some of the structured data. However, Google Search Console still shows no Rich Cards. I am not sure why, it may be that Googlebot hasn't yet gotten around to that. Or it could be that Google only creates Rich Cards for certain types of Structured Data. The documentation I found was mostly from when Google started to introduce the Rich Cards and it said they would only be generated for specific types of content - Recipes, Movies, Reviews, News Articles and a few other types. I do not know if Google has started to implement Rich Cards for other types of structured data or not. I don't particularly care about having Rich Cards displayed, I mostly just wanted to figure out how to use them.
So, while I still have no Rich Cards having the Structured Data can't hurt, and Google has started to index that and it shows up in the Structured Data report. The AMP pages have also started to be indexed, although I am seeing some inconsistencies in the Search Console Reports. It could just be that Googlebot needs more time to index things. Who knows?