In this blog post I'm going to go through the content in Google's Search Essentials Handbook.
The first thing I came across Google's Search Console this allows you to verify your actual domain - provided you own it.
You have to verify that your website is your own by adding a meta tag to your homepage. This contains the google-site-verification name and the content which I assume is a checksum.
You can click verify once you've re-deployed your website with this meta-tag, you must then wait a couple days to get the data needed.
In the google search console go to the URL inspection tab and click on Request Indexing. This will prompt Google to add your webpage to the indexing queue to be properly served on Google's search pages.