It is said that if a person were able to float in rapidly expanding space and were able to observe a region of space dropping out of rapid expansion, then this person would see a bubble universe of finite size growing larger like a balloon being blown up.

However, for a person inside of the bubble universe, it is said that they would observe that the size of the universe is infinite.

At each moment of time, for the outside observer, the bubble universe would have a finite amount of space, while for the inside observer, there would appear to be an endless amount of space.

Why is it that an inside observer cannot see that their universe is in fact finite (at a moment of time) rather than appearing to be endless?