If you've used somebody else's site builder, there may be a lot of work involved to transfer your site. In any case, you'd be doing the work - you'd need to download your files, etc., from your current host and upload them to an account you've created here. If your site consists of static HTML files, images and CSS files, or a PHP application (a series of PHP files, often with a database), the transfer can be relatively simple, if tedious. Some site builders, though, create compressed files that are only compatible with their own software, and you as an end-user would not have access to that software on your current host (so you can't download it) and would not be allowed to install it here. Worse yet, those compressed files may be encrypted using an encryption key you don't have access to in order to lock you in to a specific host. (It's not ethical, but if they inject ads into your pages, it's one way to ensure that they don't lose revenue. They can label it "copy protection" to make you feel good about it even though it's the opposite of what you want.)
I wish I could give you better news, but there would be a lot of time and effort involved. It's not the same sort of thing as transferring between free and paid plans with the same host, where it's (often) an automatic process of copying files from one server to another within the same datacentre - a process that takes a few seconds (or minutes at most). It can take many hours, depending on the size and complexity of the site, and would be as much work for anyone else as it would be for you. It may actually be easier (in some cases) to re-create the site using either static HTML files or more "universal" off-the-shelf open-source software like WordPress and a theme that matches the look and feel you want. In both cases, you can keep local backups of the site on your own local computer and would be able to upload those to another host quickly should there be a problem with whoever is hosting your site at the time.
