The cosmologists that I have read are not certain the universe will continually expand even though the rate of expansion is still increasing. Some feel it's possible to have a Big Crunch, as it's called, whereas the universe might eventually slow down and begin to contract.
Technically, it is not assumed by cosmologists that the universe began with the BB since most do believe there was likely something prior to it, and mathematical models point in the direction of our universe being smaller than a present-day atom before expansion. Also, we need to remember that we may well be part of a multiverse.
The rate of expansion is accelerating faster then light. Evidence has ruled out the Big Crunch and cuurent observations are pointing to a "Big Freeze."
Technically, it is not assumed by cosmologists that the universe began with the BB.
Cosmologiest have a "picture" of it called the CMB. The afterglow of the BB.
"mathematical models point in the direction of our universe being smaller than a present-day atom before expansion."
This is the singularity believed to have triggered the Bang. However, the BB theory only really states the universe was hotter and denser in the distant past,
not what started it. An analogy might be like evolution, we know evolution happened, but not how abiogenesis might have happened exactly.
We know the bang happened but not how it happened.
There are many good theories on multiverses, and they are looking for evidence.