When did the Big Bang happen? Did the Big Bang happen at a point? goes through the fact that the Big Bang happened everywhere at the same time. John Rennie's answer explains this as being a consequence of all points in space beings squished into a single point, so technically the Big Bang happened everywhere. But, when we talk about relativity, we also use a fourth dimension of time. So, at the Big Bang all points in space, as well as all points in time should be squished (for lack of better terms) into a single point. So did the Big Bang happen at happen 'every-time'?
Edit: The age of the universe goes into how the true age of the universe can be determined as time flows in different ways for different observers. I am asking whether the Big Bang happened at all points in time together.
 A: The real answer is that the big bang singularity isn't part of modern cosmology, in part because of the horizon problem. The big bang model is only valid back to an early era when the scale factor was nonzero; before that, something else happened. Various inflationary models are the most popular, but there are others. What these models have in common is that the state they start with isn't the homogeneous, isotropic universe of big bang cosmology (because that homogeneous, isotropic state is what they aim to explain), so big bang cosmology can't say anything about any singularities that they may have.
If we pretend that's not the case, then the answer is that the scale factor only scales the spatial dimensions, not the time dimension, so it happens everywhere but not everywhen.
A: No, the Big Bang did not happen at all points in time. It happened at one point in time, approximately 13.8 billion years ago. As you already know, the Big Bang was not an explosion in space, it was an explosion of space. However, the same is not true of time. (But if you're interested in the idea of an explosion encompassing all of space and time, then I'd recommend watching season 5 of modern Doctor Who. It's great. :)
