How do I avoid typing “git” at the begining of every Git command?

You might want to try gitsh. From their readme:

The gitsh program is an interactive shell for git. From within gitsh you can issue any git command, even using your local aliases and configuration.

• Git commands tend to come in groups. Avoid typing git over and over and over by running them in a dedicated git shell:

sh$ gitsh
gitsh% status
gitsh% add .
gitsh% commit -m "Ship it!"
gitsh% push
gitsh% ctrl-d
sh$

Or have a look at the other projects linked there:

• git-sh – A customised bash shell with a Git prompt, aliases, and completion.
• gitsh – A simple Git shell written in Perl.
• repl – Wraps any program with subcommands in a REPL.

Note: Haven’t used this myself.