Codepen by itself automatically “hosts” and “serves” it to anyone you want to see it, including yourself.
Here’s how one of my codepens looks (its just a password field) https://codepen.io/bradtaniguchi/full/jOBPWPa
However, as you can see codepen adds a top-bar to the page with their logo and tools, and its under their domain. Because of this codepen is not a production grade option, it’s more of a “sandbox” to show of specifics, but not a place to host actual sites.
Codepen is a good starting point because you don’t need to install/manage anything locally. It also provides a simple and straight forward UI to manipulate HTML/CSS/JS directly. So its easy to get going with the cure fundamentals and show it off instantly.
If you want to do anything more complex then that you probably want to start developing locally using professional-level tools. The main one being VSCode. This editor can be tricked out with extensions for more features, and can help you build what you want with the help of other tooling.
As mentioned above, you could build what you want locally using VSCode then host it on github pages, but this is much more complicated and requires much more knowledge of different technologies than something like codepen.
I’d suggest looking into jobs and see what they are looking for before applying. With only the responsive web design certificate, and some static HTML+CSS sites under your belt hosted on codepen you may have trouble finding and competing for work. This is primarily due to the small amount of positions using just these technologies, due to software like wix and squarespace being able to create full static sites without any code.
I do suggest keeping track of your pre-existing work in codepen so you do have something, but I would not focus too much on showing them off for jobs. You’ll probably need to continue learning the curriculum and building up your skills before looking back into hosting/serving your code somewhere during the job search.
Good luck, keep learning, keep building 