Can I runtime save files inside the executable file

I want to keep my game in only one file, and by that I mean save files that contain player progress trough out the game.
I can already put pck files in the exe, but can I do that?

How and why would you do that? If your executable is native code and loads into RAM, evertime you save something, you need to overwrite your own program. Even if it would work, it could bloat your exe.
When you are afraid of cheaters, try to encrypt your save files.

I never used pck files (I think so), here is the answer from an AI:

When an application is designed to work with PCK files, it has the ability to read and extract the necessary data from these packages. This is possible because the application has specific logic programmed to understand the structure and format of the PCK files.

Maybe there is somebody who can better explain it. But I hope this helps for now.

No, it’s not possible.

Any game you’ve played that had just an exe almost certainly put saves in Appdata or another existing directory

Theoretically, yes, you can. You absolutely shouldn’t. It will break depending on the file system. It is not worth doing. But you can append you save data to your executable file through a system call to cp/copy. Do not do it. You could then recover the data by using an offset into your own executable, but this will change each compilation and there are no guarantees. DO NOT DO THIS
It is possible. DO NOT EVER DO IT