The scientific answer to your question is would be that before the "big bang" all matter in the universe was condensed into a tiny fragment called "the singularity". Scientists and physicists are still trying to figure out what happened but somehow the matter exploded and began expanding. According to scientists, this occurred millions of years ago. But the expansion is still occurring so the matter in the universe has had quite a long time to grow larger. What is also interesting is that much of the matter in the universe is "dark", in other words invisible to our eyes. This means that we truly do not know how vast or immense the universe is, or even if other dimensions exist which contain other universes. You have an excellent question, one that mankind has been asking for centuries. We think we know part of the answer, but the entire answer remains unknown.
The universe is very huge, vast and immense because of the big bang.
First the cosmos was very very dense.
There was very little space.
Because of this density there was a huge exploision, breaking the limits of our universe. Thus, because of this exploision our cosmos/universe is expaning at a great speed.
And this is the reason why our universe is so vast and immense.
The universe is vastly immense as it is has 'space' between it which contains nearly no matter. The Big Bang theory states that the universe started from a singularity - an extremely dense point - and that exploded as a high speed. The matter made moved extremely far away and a high speed and that matter has not stopped moving away from the centre yet. Currently, it has been around 13.7 billion years so the universe will have spread very far apart and this explains why the universe is so big.