Site: is a Google Search Operator that is used to see if Google indexed your website. It returns the pages for that website only. Using shared economic web hosting without your own domain is a big no-no is you want to rank. It also shows a lack of professionalism as well.
I used another Google Search Operator inurl: to run a quick test and found my first candidate which is an SEO site. I ran the site: Google Search Operator and found out that Google did list the pages of that Weebly website.
If you did the same for yours then Google hasn’t ‘discovered’ your website yet to index it and that is why you see no results. A quick way to get your website listed is to provide a link to your website from a website that already gets crawled and indexed by Google.
However, if you are looking for more traffic and ranks you will have to do a lot more to achieve that goal.
Rose Si requested your answer