While it is possible that life might exist in more than 3 dimensions and be able to protrude into our spacetime (at least, there isn’t anything prohibiting it), I can only imagine such intrusions would be much weirder than the average UAP.
Furthermore, we are venturing so far into speculative territory that I’m not sure we are doing any scientific investigation anymore.
There are some pretty weird stuff out there outside the average UAP cannon — of metallic orbs, cigars and clamshells — that may qualify as your intrusions; good word!
Science lives at the edge of the unknown. In this era I think we need to engage in far-out speculation if we're going to understand what comes — especially if we hope to understand it from a non-anthropocentric point of view! Ha ha ha! :)
That we don't understand and that we never observed. This is why I mentioned we wandering into speculation territory - I really can't prove there is no invisible pink unicorn sitting in my living room right now. All I can say is that I am not observing it.
You'll see something that doesn't make sense. Then you'll examine it and start formulating plausible explanations for it, and then you may start testing those against what you know and see if they can predict what is observed in other circumstances you haven't seen before.
The important part is that the explanation needs to be testable. If we just say "something outside our comprehension", it's not usable, because you can't really test that.