Despite AMP being super fast and quick, the Google Search Console reports for AMP errors and analytics are delayed, like all the other reports in the Search Console.
Google's John Mueller responded to a Google Webmaster Help thread from someone who implemented AMP and was expecting to see it in the search results and search console.
But as you know, there are some caveats, at least now, around AMP pages. John Mueller of Google laid them out again, since this guy missed them before:
- At the moment, we're not showing AMP pages in regular search just yet. We'll get started around late February.
- In the beginning, we'll show them in a carousel with news-like content; knowing our engineers, we'll add other types quickly afterwards. (I don't know if the sample AMP page you mentioned would be seen as news-like content, so it might not be visible in the AMP carousel in the beginning -- but perhaps you have other pages that are more news-like.)
- In general, AMP pages are connected on a per-page basis (there's a "web" page equivalent to each AMP page). You can, of course, also make AMP-only pages too.
- As we crawl your web pages, and see the link rel=amphtml, we'll pick up the AMP version almost immediately afterwards. The time difference is minimal, which is great for news-like content.
- The reports in Search Console aren't immediate -- they can take a few days to update (they update at the same time as other reports in Search Console). This is why you wouldn't see a change there right after making an AMP page, even if we crawl & index it.
Probably the most interesting thing John published here that is new is the part about expanding AMP beyond news sites. It is obvious, but Google is starting with news and will see how that goes.
Of course, those who deployed AMP already are probably not good at being patient. AMP is about speed, those who turned it around this fast are also about speed. So waiting a few days for the Search Console to show you any data around AMP is likely a hard thing for early adopters.
Forum discussion at Google Webmaster Help.