Sure it's possible. It would take an infinite amount of time
So we can begin to write out all the fractions between zero and one and after some time, infinite time, we will write them all out?
After infinite time, sure. Why not?
Why do you conflate 'infinite time' with 'some time'? 'Some time' might (by a dishonest or uncomprehending person) be construed to imply 'finite time' - and clearly, if it does, then no, we will not write them all out after 'some time'. only after infinite time.
Of course, this is irrelevant to a discussion of an infinite past, which by definition does not 'begin', and so is not analogous to any activity that is described with the phrase "So we can begin to..."
So it is, YET AGAIN, a non-sequitur to your claim that an infinite past is impossible.
Have you now abandoned that claim? Because you seem disinclined to address it at all - Instead we are discussing fractions between zero and one,
which are as far as I can see, an unrelated topic.