I think that every new packaging project should start with (dist-)git repo right away, while I don't think fedpkg provides any convenient way to do it. My idea is to have something like:

$ fedpkg new-package <my-package-name>

Which would did roughly the following:

$ mkdir <my-package-name>
$ cd <my-package-name>
$ touch sources
$ git init

BTW some of the steps could pro probably aligned with rel-eng scripts which are executed on server side after fedpkg request-repo