If you're trying to use git's rebase command on your repo's first commit, you may not feel there are many options. What I found you could do is to create an empty commit in a new blank branch, and then rebase everything else off of that commit, essentially creating a new "original" commit.
The great thing here is it gets your initial commit to a place where you can use git rebase to make to make changes to it; the bad thing here is that you're modifying history, which is never a good idea for anything you've shared with anyone, especially since in this case you'll be modifying every commit in the entire repo to have a new origin of this "new" initial commit.
If you're sure you haven't shared the repo with anyone yet, and you don't mind rewriting history, here's the code:
# Create a new empty branch called 'newroot'
git symbolic-ref HEAD refs/heads/newroot
git rm --cached -r .
git clean -f -d
# Create a first commit
git commit --allow-empty -m 'initial commit'
# Rebase everything onto this new initial commit
git rebase --onto newroot --root master
# Kill off your empty branch
git branch -d newroot
And there you go! If you're doing this to add previous history to your git
repository as I was doing, this can give you what you need to add commits in
before the "beginning of time," remembering to pass --date="" when you create
that commit.
For those reading this wondering why I needed to do this, I was attempting to condense numerous copies of source code amounting to ~8.5GiB into a git repository that I could use to reference old changes. The resulting repository was ~300MiB, and came in at just over 100MiB as a bare clone for dumping on a company server.
The code I used above is taken from the current best answer to a stackoverflow question here.
Edit 2016-06-14:
This post was really intended for my own benefit, and I often come back to the page to remember how to do <thing> rather than go find it elsewhere. If you just need a new branch with no history, the following command can be used.
git checkout --orphan <branchname>
This can be helpful for repositories where one branch contains the source code
for say, a website, and another branch contains the generated content for it;
this site uses a branch named generated with its own history for this purpose,
much like the gh-pages branches that sites hosted by GitHub use.
Note that as of git 2.9.0, git will refuse to let you merge this new branch with
an existing branch; the intent here is that if two branches have no mutual
history at all, merging them is likely a mistake. If it isn't a mistake, add
--allow-unrelated-histories to your call to git merge and it will let you
merge them.