I have some error I heard I can install Unreal Engine 4 without Epic Games Launcher.
Most common mistake!
To install engine without launcher by compiling the source, you should follow procedures as noted here
Its a private repository so you get that error.
I tried this method,but it’s not working.
It is a wrong link in the epic documentation. Correct one is this Downloading Unreal Engine Source Code | Unreal Engine Documentation
Is this gonna work even now in circa Anno Domini of year of 2021?
yes, you do not need to use the launcher to get the engine.