Now, let's say the website admin does not submit their sitemap orother domain related things/URLs anywhere and even then the searchengines index it
The ONLY way Google discovers new URLs is via links (from websites, sitemaps, etc.,). Still, if Google can crawl and index, there is only one possibility. There exists a link to the website from a property not controlled by the website owner, period. Unless there is a link to a website or a sitemap that is explicitly made available to Google, the website will remain in dark forever.
Ref: https://developers.google.com/search/docs/beginner/how-search-works#crawling
The first step is finding out what pages exist on the web. There isn'ta central registry of all web pages, so Google must constantly searchfor new pages and add them to its list of known pages. Some pages areknown because Google has already visited them before. Other pages arediscovered when Google follows a link from a known page to a new page.