There can be several reasons causing structured data not appearing in Search Console, besides having them validated. The fact that Google will crawl your page doesn't assure that they will show you the structured data as the other answer suggests. There is no an estimated time as this is a process that Google doesn't specify in detail how they handle and validate them internally.
Google does not guarantee that Rich
Snippets will show up for search results from a particular site. Here are some reasons that marked-up
pages might not be shown with Rich Snippets:The marked-up structured
data is not representative of the main content of the page or
potentially misleading.Marked-up data is incorrect in a way that
the testing tool was not able to catch.Marked-up content is hidden
from the user.The site has very few pages (or very few pages with
marked-up structured data) and may not be picked up by Google's Rich
Snippets system.
Q: How long does it take for rich snippets to be visible? A: Once
you've marked up your site's content, Google will discover it the next
time we crawl your site (although it may take some time for rich
snippets to appear in search results, if we do choose to display rich
snippets for your site). If you're marking up your content for rich
snippets, you can let us know. Google won't be able to individually
reply to your message, but we may use the information you supply to
improve our detection and display of marked-up content
If you have validated your structured data, and you are sure they are relevant you only need to wait, check for it in few weeks.