There are different reasons why you can't find your own homepage on Google.
Does Google already know your page?
Of course, the search engine first has to know that your site exists. You can find out if Google already knows your site by googling for "site:here-insert-your-URL". If Google then lists your site, the search engine already knows your homepage.
If Google does not know your site: Google usually finds out automatically by Google's so-called "crawler" following links on the Internet. This means that if there are websites that have set a link to your page (backlink), your website will naturally be listed faster on Google.
The age of your homepage
If you have just registered your own homepage, and in the worst case you have not even published any texts or edited any pages, then the search engines will not be able to find you when you enter your page name in the search box. You should have a little bit of time here.
The content of your website
Probably the most important point for the findability of your website via search engines like Google is, of course, the content of your website. "Content is King!", which means "Content is important!" is more important today than ever before.
After all, what is a search engine supposed to "read" on your site if you have little to no content published there? Right, nothing. Also many pictures on a homepage bring only conditionally something with the findability by search engines, since the "Crawler" can look at no pictures, but only text contents read out.
And if you have only registered a free website with us, then this is probably the reason, because our free pages are not released for the results of the search engine providers and can then not be found. Please refer to this article.