It is an easy answer.
If there was a Big Bang, a singularity spread out matter from one single point, such as particles being flung from a spinning disk.
It would mean that this matter will spread out into space in a spherical model, and will continue to travel away from its central point.
This means that no matter when, even billions of years from now, that sphere will only grow larger and less dense.
This is the Big Bang model contained within the laws of ennergy conservation.
If not the above, which renders a finite universe, then matter appeared throughout the universe, everywhere at once, and the Big Bang model never happened.
In that case, we will not have any clues whether the universe has a boundry, and it might be infinite, and finite.
In any case, I believe the universe to be finite due to the observable nature demonstrates that everything we know so far, has boundries.