There's no point in starting early. Most people burn the first year of their PhD doing coursework, satisfying teaching requirements, and learning about a topic to even just come up with good questions. You can't really study to get ahead. It's a marathon of continuous work to understand the current state of a problem and then to come up with a novel solution. You need to go in rested (take a vacation) and ready to go (get your housing settled, move in, set up new insurance, licenses, etc...) So that you can hit the ground running and keep running.
If I were you, if you have the money to survive the first few months until the stipend kicks in, I would take a nice, super memorable vacation. If not, I would find a way to take a cheap trip with friends.