You have made no argument showing how it is possible for there to be a present moment even if the time before it is infinite.
Nobody needs to do that. If you don't think an infinite past is possible it's up to you to show why it is not possible.
HINT: usually, this involves logic...
Specifically, you have to show that the concept you want to attack is somehow self-contradictory.
That is not at all how it works.
If somebody claims that it is possible for there to have been an infinite number of moments in time before the present moment THEY have to show how this is possible.
If somebody claims they climbed an infinite number of stairs before the stair they presently stand, THEY have to show how this is possible.
If somebody claims they had an infinite number of children before the child they hold, THEY have to show how it is possible.
The believers in real infinities have to show how any could be possible.
In no way do we assume that ANY are possible without a demonstration.
Notice that nobody cares if you proved that your own private concept of an infinite past is wrong.
What I notice is that YOU don't have any interest in defending what are incredible claims. Claims like, an infinite amount of something can be encased in a finite container, that an infinite amount of time ("A" in my little graph) can be contained and bounded by the present. You possibly think this is possible because you don't know my little graph is a complete abstraction of the situation. It uses lines of finite length to define lines of infinite length.
Basically you claim that infinite time isn't really infinite. It can finish at the present moment.
And you think you can somehow get away with this by saying you will define an infinite amount of time as time that never starts, whatever that could possible mean. You think by defining infinite time this way it isn't really an infinite amount of time. It is an amount of time that finishes. Since ALL the time that has occurred in the past ends at the present, saying an infinite amount of time occurred in the past means an amount of time that never finishes finished.
It is an absurd claim.
So you first have to understand the concept of infinite past that people are using, for example the one assumed by scientists before Einstein. Do you?
People presenting what they think Einstein means isn't at all convincing.
Relativity is about speed and light and what happens when the speed of things made of matter approaches the speed of light. It is not a proof or argument of any kind that infinite time already passed in the past.
Is it possible to count to the end of the negative integers before some point in the future?
How did infinite prior moments finish passing before the present moment?
...we don't have to show that it would still be possible to count past years if the past was infinite.....
Here is where you are dead wrong. A year is an amount of time. If time always existed then the passing of years of time always existed, even if there were no people to record those years.
And if time is infinite in the past that means that an infinite number of years passed before the present moment.
It is quite funny to see that in your analogy between an infinite past and the set of negative integers, YOU JUST CHOOSE to ignore the fact that the infinite set of negative integers ends at the number 0 just like an infinite past would end now. By your own account, you have just definitely shown that the set of negative integers cannot possibly be infinite although for some mysterious reason you only fathom you see no problem with the future being infinite as you don't see any problem with the set of positive integers being infinite. Your argument has to be ridiculous.
EB
The negative integers DO NOT end at zero.
They BEGIN at negative one. There is no end to the negative integers, just like there would be no end to the past if it was infinite. It could not end at the present.