Get Github Pages Site found in Google Search Results

It can take a few days before the site is indexed by search engines. Google for google index site and you will find quite a lot of information about the process and how it can be speed up.

You have to create a Google Search Console account and add your page, then typically you just drop a "marker" file in the root (Search Console generates this) so that Google can confirm you really own the page.

Google Search Console

Instructions

(Since the instructions are long and have many links to sub-steps, I'm only providing the link.)

Also, if you're going to use a registered domain name, set that up before you register the site for search.

(Edit: Technically you don't have to do this, sooner or later Google will find you... but this will give your content a much higher-quality score.)