How long until Google sees a new site

Google does not publish a mandatory waiting period for a new site. A page can be crawled within days of a sitemap submission. Showing up for a phrase that already has older pages is a different story, and it does not end on launch day.

Crawl, index, and appearance

A crawl is the visit. Indexing is the save. Appearance in results is the choice to show the page for a query. The three do not happen together. A page can be indexed and still not shown for the phrase you wanted.

Google has no document that says "a new site is hidden for 90 days". What does happen: a site with no links and unverified ownership takes longer to be discovered. Search Console verification and a valid map shorten discovery, not the competition.

Three different stages
StageWhat it isA sensible range
DiscoveryGoogle finds the URLDays after a map and verification
IndexingThe page is storedDays to weeks
Showing for a competitive phraseThe page is chosen over othersWeeks to months, with no promise