I would recommend getting your Google Search Console and Bing Webmaster Tools accounts setup:
Search engines will eventually find your site if there are links to it on other websites however you can manually submit your site for indexing by Google and Bing via the URLs above. The tools above are also useful to track and understand how your SEO efforts are effecting your site's search presence. Additionally after you register, the search engines will notify you if they find search related problems with your website that may effect ranking performance.
It's also worth setting up some additional tracking measures, such as Google analytics
to gather more information about your site's performance so that you can see the results of your efforts and find areas for improvement. Do be aware of the privacy implications of Google analytics though, particularly in the context of GDPR and cookie privacy laws.