Is there a way to remove all commits before a specified commit and use that commit as the initial?
Let's say the new oldest commit's hash is X and we can use "oldroot" and "newroot" temporarily:
git checkout -b oldroot X
TREE=`git write-tree`
COMMIT=`echo "Killed history" | git commit-tree "$TREE"`
git checkout -b newroot "$COMMIT"
git rebase --onto newroot oldroot master
# repeat for other branches than master that should use the new initial commit
git checkout master
git branch -D oldroot
git branch -D newroot
git gc # WARNING: if everything's done right, this will actually delete your history from the repo!
That will create a 'newroot' commit with the same contents as the 'oldroot' commit, but without any parents. Then, it rebases all the other branches onto the new root, which should be in the history of all of them.
EDIT: tested and fixed; slightly later, refined a bit