Your comments about it being "obvious" that there are more numbers than even numbers is a bit misguided.
The fact that there is a one-two-one correspondence shows that the Cardinality of the Natural Numbers is the same as the Cardinality of the Even Natural Numbers.
It is not obvious that the Cardinality of one should be different than the other. Cardinality is not "size", or "amount". It is a statement about the existence of a bijection/surjection/injection.
Your problem is that you are confusing the word "cardinality" for the word greater. This is incorrect.
There are many notions of greater in mathematics, besides cardinality. It is unfortunate that in common media, Cardinality is expressed as expressing an amount of something.
It ends up computing amounts in the finite case, but it is a much more generalized concept than amount- and there isn't any reason to expect it to look anything like a notion of amount in general.
Of course, even if it was in general a notion of amount - there is no reason to expect that non-finite amounts behave anything like finite amounts.
Your analogy is conceiving of infinity as a never ending process, and noticing that even if two processes are never ending- one may "grow" faster than another.
This is a concept well known to mathematicians, and is covered in the case when they study infinite sequences, a faster growing sequence "dominates" a slower growing sequence. The study of limits in Calculus takes this notion, and formalizes it to great effect. In this sense of infinity, we see many mathematical models projecting behavior as things get arbitrarily large or small- which is essentially the defining notion of calculus. Infinity here, means arbitrarily large. If the universe will last forever, then it is possible this notion of infinity is realistic. As, it makes sense to say- after an arbitrarily large amount of time, x happens. etc
This is a very distinct notion than the set theoretic infinity, which is not about a never ending process. Set Theoretic Infinity, is about considering collections of objects, defined by a property- for which infinitely many distinct objects satisfy.
So, if we take the collection of "all events that will happen in the universe"- it's possible that such a set is, literally infinite- and makes sense as a claim about the real world.