I really do not believe my question is so hard to understand. Let me try again:
I think your question is very hard to understand. You appear to be making assumptions that do not fit with either biology or theology and then you wonder why we can't make sense of your question.
The history of evolution is 10^10 years long. And human appeared at the very tip on this line of evolution.
All of a sudden, the salvation arrived now.
Why now? Why not a little bit earlier or later?
Why earlier? Why would salvation be needed earlier? What would it be for? What did the world need saving from before humanity sinned?
Why later? Well, actually it was later. Atonement for sin was made at the cross only 2,000 years ago. So it was later.
Imagine the salvation were a knife dropped from the air onto a long long line, what is the chance for it to hit the very end of the line?
Why resort to a misleading image of salvation? If salvation is a "knife", God did not drop it; he aimed it and aimed it truly.
If you try to say: God decides. Then you are not answering the question. You have to give a good reason to this statistical oddity if you emphasize evolution. Or, you like to raise the argument of sin (no sin, no salvation needed). In fact, that is a bad one, because it would be even harder to explain "the evolution of sin".
I think much of your problem is that you are trying to understand evolution as something spiritual as well as biological. It's not spiritual. It is a physical, biological process. Giving it spiritual status and thinking in terms of evolving a spiritual relation with God is rather like imagining a spiritual aspect to the erosion of a riverbank by the movement of the water in the river.
Keep in mind that biology is one thing; spiritual relationships are a different thing. Evolution is about biology, not spirituality.
Now as to your question--it is about a spiritual matter: salvation. Salvation only makes sense in the context of needing to be saved from something. Until there is a spiritual danger, a spiritual trap from which we need to be rescued, there is no point in speaking of salvation.
There is no evolution-related statistical oddity in God's choice of the timing of salvation. Paul tells us plainly in his letter to the Galatians, that God sent his Son "when the fullness of time had come". (Gal. 4:4) What does this fullness of time have to do with evolution? Were the humans of 2,000 years ago a different species than Adam and Eve? than Moses or David or Isaiah? Of course not. Evolution has nothing to do with how God determines the fullness of time for salvation. Because evolution is about biology, not about our relationship to God.
Nor is it hard to explain the evolution of sin, because sin is also a spiritual state, not a biological condition. So sin is not a consequence of evolution at all. Therefore there is no need to explain sin in terms of evolution.
This question would be answered, IF, we have existed at least 10^8 years, or even 10^7 years long. The longer, the more reasonable.
A better alternative is: Human being is NOT evolved, and is a special creation. This would give the very very odd statistics a lot more sense.
Rather you are trying to use statistics when it is inappropriate to even consider the matter statistically. We have no basis for measuring sin or salvation statistically.
So your conclusion does not apply, for the specialness of humanity is not biological. As a biological species, humanity is unique, but only in the sense that every species is unique. A bacterium, an ant, an owl, a pine tree, a paramecium, or a pumpkin can each also be called unique, since there is no other species exactly like them. The biological uniqueness of humanity is not what makes humanity special.
For the same reason, the biological-evolutionary origin of humanity does not stand in contradiction to our unique spiritual relation with our Creator. Since our evolution deals with our biological being, it has no relationship, either positive or negative, on our spiritual connections with God and with the creation in which we find ourselves.
Notice that this question is particularly aimed at TE. If there is only E without the T, then this question would be invalid and not belong to this forum.
When you disentangle biology and spirituality and deal with each appropriately, you will come to the correct relationship between the T and the E. There is not only evolution. There is also a unique relationship, a unique calling for humanity. But evolution is a biological process apart from the spiritual endowment we have been given by the grace of God. One cannot insert that spiritual reality into the science of biology, nor treat it as if it were an aspect of biology.
One must respect both the scientific reality and the spiritual reality, but not try to treat them as if they were identical and can be analysed in the same categories.