Our corporate PCs have git installed which always tries to gain admin access on any git command, Even git --version. This is weird that git is designed that way that it need admin access for any git command.
We have Beyond trust privilege management which keep tracks of any application which tries to take admin access, this process takes a very long time to verify and because of this git works very very slow in all PCs.
Eclipse has its own integrated git which works fast as it doesn't take admin rights to do operations.
Is there a way we can run git without admin rights in Windows 10?
Not only is it possible, it's perfectly normal.
There is an official Windows installer for git here: https://git-scm.com/download/win The installer requires admin access, but once installed, commands will run as a normal user.
There is also a "portable" version, which is a self-extracting archive that can be extracted to anywhere on your system, so doesn't even need admin permissions to install.
It sounds like your install of git has been installed with some additional permissions set such that only an admin has permission to the executable. That would be something to speak to your system administrator about.