There does not appear to be a way to accomplish what you want without using a bridge tool to connect Git with Perforce.
I am in the same situation as you in my current job and we have considered trying out a Git-Perforce bridge. Perforce has a bridge to Git called git-fusion
which is free for up to 20 users. This is probably the best bridge tool there is. Git itself provides a command called git p4
which gives you some more limited functionality. Your workflow using git p4
will look something like this:
# do your work and make your git commits
git p4 rebase
git p4 submit
As you might have guessed, git p4 rebase
goes to the repository and gets all changes made by other users in that branch before committing your work on top. Rebasing is necessary because it simulates Perforce where all of your commits always remain intact.
If you decide to go with a bridge tool, realize that this will likely a big IT infrastructure change and you may have to convince your organization that it is worth undertaking.