To show in Google AI Mode & AI Overviews, your page must be indexed

In order for your site to show in the citations and links section of Google AI Mode and AI Overviews, your pages must be indexed by Google Search. At the same time, just because your site is indexed, it doesn’t necessarily mean that Google will show your page as a link n the citations section of the AI Mode and AI Overviews.
What Google said. Google posted these details in its help documentation over here, on the topic of AI features and your website. It reads:
To be eligible to be shown as a supporting link in AI Overviews or AI Mode, a page must be indexed and eligible to be shown in Google Search with a snippet, fulfilling the Search technical requirements. There are no additional technical requirements.
Google added:
Just because a page meets all requirements, best practices, and complies with the policies, doesn’t mean that Google will crawl, index, or serve its content. Indexing and serving isn’t guaranteed. Learn more about How Search Works.
John Mueller from Google also said in a comment on LinkedIn, he wrote:
In general, yes, it has to be indexed in order to be shown as a link there. The requirements we listed are basically for when you’re starting fresh: if you create a URL today, what do you need to do to be eligible to be shown? (and like most things in search, eligible to be shown doesn’t mean it’s guaranteed)
What are the supporting links in AI Mode? Here is a screenshot to make it easier to visualize:

What are the supporting links in AI Overviews? Here is a screenshot to make it easier to visualize:

Testing. Dan Petrovic also tested this to confirm this is true and he wrote:
This strongly suggests to me that when Google’s AI Mode (or its Python execution environment) attempts to access a URL, it doesn’t necessarily perform a fresh, live HTTP request to the target server every single time. It seems more likely that it first consults Google’s vast index or a cached representation of the web.
Why we care. While this is likely obvious to a seasoned SEOs, it is important to remember that a page does need to be indexed for it to show up in these AI results within Google Search. So while there is a lot of chatter that SEO is dead, for a site to show up in these AI results, you need to make sure your pages are search engine friendly.
Will you get traffic from showing up in these AI responses is a different story.