I'm not sure where you've picked up this idea, that proof is required for claims of existence but not for claims of non-existence. Basic philosophy dating back at least to Aristotle. Not to worry, I can provide some assistance. Check out the links below to find an extensive bibliography of basic texts you can consult and listings of some of the more common logical fallacies. Then, come back and run your story by me one more time.
Current theories hold the universe is finite in size but has no boundary.
After doing this 360,000 times, I'll start new lines, each at a new interval of 0001 of a degree, and then .00001, and then .000001, and so on. This is incorrect and demonstrates a poor grasp of basic mathematics. Since the universe is finite in size and since a toothpick is a physical object of non-zero size, you will eventually fill the entire available space within the universe with toothpicks. The fallacy in your argument comes from the fact that you are assuming that physical distance is infinitely divisible. In fact, what you're arguing is actually a variation of the famous Xeno's Paradox.