There are many kinds of quantum weirdness. One of them is this: we think classically of the past as definite and the future in terms of possibilities- but in reality both the future and the past are indeterminate in exactly the same way (it’s just that typically there are a lot more possible futures for the current state than pasts, because of entropy). In fact you could define the past as being the direction in configuration space with the smallest uncertainty, and the future as being the direction with the most uncertainty. In this view, at the Big Bang since there is no direction with less uncertainty, there is no past at that point.
That’s not the only quantum weirdness, but it’s a big one.
That’s not the only quantum weirdness, but it’s a big one.