You can absolutely do that. If you want to upgrade to a paid plan to get some of the features you want, then you can switch at any time through the My Products option in your account or with the help of a GoDaddy Guide. Once you upgrade your site will have all the same customizations and work that you've already put in place, just with the added features. See Website Builder plans and pricing for more info.
How to create a Website in Google Sites for Free