Just attempted this same strategy in pretty similar SVN --> Git migration scenario, but I encountered a "dubious ownership error".
The strategy we used was I git SVN cloned the repo to import the revision history, had everyone pull an update in SVN, and did a final git svn fetch/rebase to get the git repo synced with SVN one last time. Then, I zipped the .git folder from my local repository and emailed it to all team members. This way when the .git folder was placed in the root of the project directory, the remotes and upstream branches would be pre-configured, we would not have to go through the trouble of configuring and setting up a new project from scratch as the project is old and it takes alot to get a new project actually running, and it would (theoretically) recognize only the pending changes each person had thus eliminating the need for us to have clear working directories.
However when we unzipped the folder into the project, it refused to recognize as a git repo because the repository was linked to me and my computer, stating "Fatal: dubious ownership error"
The only ways around this I can think of is either
To have each person clone the entire repo from Github, then copy the .git folder from the cloned directory into the deployed project, as that .git folder would be assigned to each user.
run the command git config --global --add safe.directory <absolute path to project directory>
on each person's computer, but I have read that this can be buggy.