Index your site on the smallweb/indieweb search engines: https://indieseek.xyz/ https://wiby.me/ https://plumb.one/ https://www.yioop.com/ https://infotiger.com/ - one those (I don't remember which) has a captcha but no confirmation if the submission was successful so no idea if it's working :P
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prepare an alias for these because they want your email: https://www.anoox.com/search.php https://blue-pages.bitbucket.io/ - the last is more bureaucratic (also requires a social media as second method of contact, well, you can give wrong link by mistake.
Rembering you can also index your site on Google Search Console (StartPage uses their index), Bing Webmaster Tools (DuckDuckGo and Ecosia use theirs), Yandex Webmaster, and also queue your site for crawling or Marginalia-Search by searching "site:yoursiteaddress"
as far as I know, you can't request indexing on Brave and Mojeek.
you may also feel like you fit this index https://theuselessweb.com/