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.
As far as actually doing the nuts and bolts building and design of your site, you also have plenty of options. You can hire someone to design and code a website, or you can try your own hand (if you're a novice, The Best Courses for Learning How to Build Websites is an excellent starting point). You can use an online service to create web pages, or build it offline using a desktop software tool. Or, if you're a coding dynamo, use a plain text editor to create a site from scratch. How you mix and match these decisions depends on your skills, time, budget, and gumption.
You may expect a 404 page to pop up from time to time on new websites, but with patience and determination, you can build a fully functional, beautiful, and highly converting site from scratch. The main takeaway here is always to test your website before launch and remember that refreshing and revamping your website is a task you will have to perform regularly from now on if you want your business to grow.
How To Make a WordPress Website - For Beginners