Question

Can I make bash to suppose the command always to be a git command?

I mean:

If I wrote push origin master then it would execute git push origin master?

Note: I would use it in git bash (Windows environment), so I do not need regular commands (ls, cd, etc.) to work.

Answer 1

You may want to try this small git shell, instead:

gitsh () {
    while read -r -p "gitsh> " -a GITCOMMAND; do
        git "${GITCOMMAND[@]}"
    done
}

After that function is defined, run it once, and it will sit in an infinite loop,
reading a command line and passing it as options to the git command.

EDIT: Adding the -e option to the read command, as suggested by gniourf_gniourf, gives you a nice Readline-based environment where you can retrieve and edit your history.