First, install the runInTerminal extension.

Then, add the following to your keyboard shortcuts:

{
  "key": "cmd+shift+p",
  "command": "runInTerminal.run",
  "args": {
    "cmd": "git add . && git commit -m \"`date`\" --allow-empty && git push",
    "match": ".*"
  }
}

• && will wait for the previous command to finish before executing
• git add . will add all files to be commited
• git commit -m \"`date`\" --allow-empty will commit with the current date as a message even allowing commiting no changes (important if you’re just creating a branch without changes)
• git push pushes the branch

Final note, I published this blog post with that keyboard shortcut :)