People are not traversing all of time. People do not need to traverse all of time for time to exist prior to the existence of people or after people no longer exist. Your example is not valid. Please stop using it.
You have no valid criticism. This has nothing to do with people traversing all of time. It is about the impossibility of infinite time. The impossibility of any infinity actually existing.
You cannot traverse any infinity. You don't actually have to imagine anything to understand that.
An infinity is not something that anything can traverse. Even time itself.
There is no such thing as a real world infinity. It is not a real world concept.
And those that claim there are have no evidence for their delusions.
Except of course for a thing which has existed for an infinite amount of time. We humans don't exist as units, for an infinite amount of time, so we can't conceive of us going back forever.
But time doesn't play backwards. However if we do a thought experiment, we can imagine going back in time, and never finding a beginning. And just how long (?) would one have to go back, (in imagination), before one could reach the conclusion, "You know what, this never ends, (or never starts to be more accurate)".
Of course to speak of going back to the beginning is nonsense, (if time-past is infinite), because there would be no beginning. But suppose time-past
is infinite - we'd have no way of knowing what it would be like, and no way of knowing if it were impossible or not. So all we can do is speculate. Some cosmologists have proposed that time-past may well be infinite, or beginningless. And good gravy, what differences might there be in the nature of reality, if time-past were indeed infinite, if we could travel back over time for a look-see. The very nature of time itself could be different, varied, unrecognisable by our standards and experiences, as we recede, (if we could arrange it), into the dim recesses of time-past.
It is also pointless to say that if time-past were infinite, that it could never reach today. That implies that there is a point of time in the past, from which we could never reach today. But going backwards, we could never reach such a point in time - it's a nonsense, (in an infinity of time-past).
The mathematical concept of a line, is an infinite series of points, and yet we
can go from point 'A', to distant point 'B' on any such line, ('A' and 'B' are separate and on that line). Of course, points are of size zero, so we can fit an infinity of them into a finite interval. But the concept of a
moment in time is also zero, being the boundary between time-past, and time-future, and yet itself being neither past nor future, and of duration zero. A moment in time is neither
then, nor
to become, but is just a location on the time-line, as a point is neither left nor right, but is just a location on the spatial-line.
So a moment in time is the interface between past and future, just as a
plane is the interface between one volume of space and another. Yet the plane has only two dimensions, and
no thickness. So a plane has no scalar measure perpendicular to itself. It's a boundary, just as there is a boundary between time past and time future, also with zero dimensions perpendicular to the time-line. But being of size zero, there can be an infinity of moments between any two designated non-identical points on a time line.
As for evidence, it's like creationists asking for direct experiential evidence of one kind of animal evolving into another. No one lives long enough to have directly observed a hippopotamus-like animal evolving into a whale. But that doesn't mean that it's not true. One has to seek other evidence. In the case of a beginningless cosmos would have to be a mathematical one, I'd suspect. At least a mathematical model, consistent with our current knowledge of physics, which allowed for infinite time-past, would point to it
not being impossible.
