A bigger vacuum chamber, which you can find plenty of, can have a volume of around a cubic meter. The gas in a pocket-sized, uninflated balloon is no more than 50 mL. That gas, if it comes out of the balloon and fills the chamber, will still leave it in a near-vacuum state (I won't post calculations). But nevertheless, you'll be seeing the balloon fly first, before its gas left it.
And what I did, I have said already in a post but I guess you didn't consider it much, was laser propulsion. High powered laser in a vacuum, attempt to measure the thrust it produces. Not unile a rocket. If a laser rocket works in a vacuum, you can be sure a liquid fuel rocket works too.
As a sidenote, again, I already said that outer space doesn't have zero pressure. There is some, though not much. We can create much, much more perfect vacuum in a vacuum chamber.