It's the same way you get any page into Google's search results. You can either wait for it to be indexed, or submit it manually. As long as you're supporting the protocol, there shouldn't be a problem. AMP pages have a custom attribute in the <html> tag that lets Google distinguish them.
You can also link your pages explicitly, as described here.
My understanding is that this markup will trigger Google to add the page to their own cache and present a link to the page in their cache in the search results. (The search result pointing to "google.com/amp/...", the page showing the infamous header, etc.)
I don't see how you can use that to get other caches (or even just the original AMP page) into Google's search results.
(Sorry if I'm mistaken though)
> The cache acts as a CDN to improve page speeds, but isn't a requirement for indexing.
How, as a site author, would you control that?
Is there a way to use AMP but explicitly opt-out of caches? I'm not aware of one. (Short of deliberately violating the AMP spec, but then you can't really say you're using AMP anymore)
By having the "desktop" version of the site (which has a high PageRank) point at the AMP version of its pages using rel="canonical", perhaps? (And then the AMP version could redirect desktop viewers back to the desktop site.)