Better way to find commit from tarball?

Someone handed me a tarball that represented an unknown release from a project. Here's what I came up with to identify the commit:

    cd $SOME_WORK_DIR
    find . -path ./.git -prune -o -print0 | xargs -0 rm
    tar xvfz $TARBALL
    for commit in {0..100}; do
        id="master~${commit}"
        if git diff --quiet --exit-code "$id"
        then
            echo "Matched on commit $id"
            break
        fi
    done

Someone please tell me there's an easier way to find a matching tree when handed a tarball. This works, but seems cumbersome.