Forget about free domains if you want to do something remotely serious with them. A real domain is few dollars/year and AFAIK you could use it coupled with GitHub Pages for simple, static websites or with altervista.org if you need WordPress.
I second GitHub Pages!
I host a professional website/online CV there with a dot com domain for less than 10€/year.
There are Jekyll templates to do that or pay someone to make you some custom CSS and Html that's easy to maintain.
I feel like there's an inherent misunderstanding in your query. If you want to run on your own domain - you run your own stuff (for the most part). You need a webserver, that's about it.
Domain registrations are not free. It's an annual fee, I don't think any company will give those out for free.
I can recommend using https://www.namecheap.com/ for domain registrations.
As a developer: google sites is 100% the exact same as wordpress, just looks better.
I’m not gonna slander you for not knowing the difference between a host and a content management system.
The issue seems to be that google offers a pretty foolproof experience for people with limited technical knowledge. That is not the case with the majority of open source systems.
Additionally: from what I hear, you wont get free top level domains with sites and not with other providers so please accept that you wont get this for free.