The big problem with this reasoning is that you are applying a property that applies to everything within the universe to the universe itself.

That's called science. Applying principals which have survived repeated experimentation and observation to the rest of the natural world. We have no reason to believe the universe operates differently. There is no proof suggesting as such.

To suggest otherwise in this sense goes against Newton's laws, as one would suggest there is no reaction to cause an equal and opposite reaction - no catalyst. Same with the laws thermodynamics and the law of the conservation of energy. Energy can't, that we've ever seen, be created from nothing. And there is no evidence pointing to some infinite energy source.

The universe exists outside of the universe, where there isn’t even time

This is not proven and is heavily debated. The "edge" of the universe, should it exist as such, is elusive to our analytical instruments since we are unable to view past the observable universe. It's likely infinitely expanding, but we don't know what that means or how it looks. Look up Ballooning Universe, Higher Dimension Wrapping, etc. Be careful not to suggest that things that have only been surmised are true, without any fact backing it up.

There is absolutely no reasonable way to conclude that the universe had to have some kind of cause.

There is also no reasonable way to conclude that it didn't have to. In fact that would be the anomaly as it would go against everything else that is observable in the natural world.