You havn't proven anything so far. All you've said is "Nothing doesn't exist" with no logical structure or following to show how you've come to that conclusion.
You claim that non-existance cannot exist? So everything exists then? Even purple monkeys with pink poker-dots. Nope, they don't exist. So they are non-existant. Wow, I just labeled something non-existant and the label was correct, so non-existance does exist!
Again the claim that there is no outside of the universe, and that the universe are eternal are so far not backed up at all.
While I'm not saying you're wrong, I'm saying that you cannot take your proofless stance without considering my proofless stance as possibily being true as well. Thats the thing with stuff that can't be falsified.