Hello, I created a map on CryEngine 5.5 . I would like to know how I can start the server so that other people, on the Internet, can connect to me?

Very long road for you. There is no simple way to implement networking to Cryengine. You need to code it. And when you finish, you need External IP address for the other to connect to you

Not to mention that their system is flat out buggy, bad RMI's, bad option groups, etc. etc.

Lots of issues that I've had to fix in the engine source code.....and I'm STILL working on it!

In fact, you can't reliabiliy implement networking becuase their core timer system is inaccurate. As in, client/server diverge near instantly.
1) Floating point errors, catastrophic cancellation, rounding, inconsistent sleep rates (e.g. 0.065 vs 0.0073 seconds, obviously they're diverging. Every frame. Pretty fast.....)
2) Physics thread has a giant 'TODO' on fixed timesteps/thread-syncing. That hasn't been touched in ages .-.

And so on.

Currently overhauling the engine to improve the timer system, in final merging/pull request stage. Should have it out as soon as possible, was hoping 3 months ago but RL kicked in. So, dunno, a month?
Doesn't help that nobody has a decent work flow with github, or a work flow period. Then again, seeing how most people 'debug networking' code (e.g. open each window by hand and drag them around) vs my method -> Press 'debug' and boom 3 windows instantly in proper positions...... xd

Yeah. Cryengine networking system is very very bad. That's why I stopped using it. I implemented SpatialOS platform networking into the engine which is mind blowing. Also they allow unlimited access to small server (8 core) so you can upload your server and run it online.

Hmm, never heard of that implemented.

Sounds like another 'we host it crappily for you and charge $$$$' solution.

I also dont' see how that would work around CE networking, unless they have a custom interface just for that? I mean, you're gonna have ot use aspects/etc. anyway?

Nope. With that you don't use any networking frm crytek. You still do run server, but headless mode just so server instance simulates stuff. They charge for full release if you want to run massive server, and that's obvious. Those things cost. But they give you unlimited access to small server that you can use 24/7. It is highy speed network really. You implement their netwoking system entirely. Their interfaces handle networking. You just have to implement them the way you want. Their system is specialized for gaming only and it is based on the concept of entities+components which makes it much easier to implement for current cryengine. And there much more to it. They allow you to have multiple server instances to simulate single world, so that everything is splitted between multiple how they call "workers", positioning and interests of the server workers can be widely configured, and can automatically split tasks using load balancing. You definitely check that out. They are not bullshit. And their support is just amazing. Servers worldwide. You can choose which server you wanna use anytime you run it.

Regardless you don't have anywhere near the amoutn of control/tracability/debuggability as you do with stock CE.

Knowing how you did networking (e.g. "I dont know how or why this works but I did it like this") it's hard for me to trust that this is a magical fix-all

You have just as much control and debuggability as with stock ce. Why? Because you can run it locally. You don't have to upload it to their server. In fact, I upload after I do multiple tests locally. So basically nothing absolutely stops you from attaching debugger to the cryengine server worker running locally EXACTLY as you do it now. There is literally no difference in this regard. After uploading, some tests are also possible, because you can access your server from your browser. And you have multiple options there. You can define server flags, you can log from cryengine to their log system that you can follow in real time.
Their documentation is very well written, so you can right away see how they do things if youre so skeptical.