If voltage can exist while current is 0...?
The clue to voltage is in it's proper name: Potential Difference.

Voltage isn't a real thing, it's just the difference between two things.

Imagine, if you will, a tank of water.  Say it's 1m on each side, and you fill it to a depth of 10cm.  You lift the tank up off the ground to a height of 1m.  So the top of the water is 1.1m above the ground.

Now you make a hole in the bottom of the tank.  The water flows out of the hole.

Until you had made that hole (created a circuit) the difference in heights still existed.

Now imagine the same scenario, but you instead fill the tank right to the top.  The top of the water is now 2m above the ground.  You have a greater potential difference between the top of the water and the ground.

Make the same hole, and the water comes out with more force due to the increased weight of the water in the tank - the greater potential difference causing greater current to flow.