You can run git-log --name-status, which echoes something like:
commit afdbbaf52ab24ef7ce1daaf75f3aaf18c4d2fee0
Author: Your Name
Date: Tue Aug 12 13:28:34 2008 -0700
Added test file.
A test
Then extract files added:
git-log --name-status | sed -ne 's/^A[^u]//p' | sort -u