I think I understand your question. I’ll try to answer it the best I can.
You question is based on the assumption that God's existence is compared to an infinite time line. He was here for an infinite amount of time and He will forever remain here, but at any instance He experiences only the ‘now’. Yet, if we describe God's existence as an infinite time line, we run into problems. If we point to a specific point on this infinite time line, we can evaluate two things: one, a list of historical events which have occurred up until this point. And two, that God has existed up until this point in time, albeit an infinite amount of time. We do not know, however, if He will continue to exist. That is one problem with your theory; as Jews, we DO know and believe He will forever exist.
Another problem is the following: Free will aside, we know that God knows what we will do before we do it. If I decide to pick up a pen, God knew that (forgive the past tense), before I even picked it up. If your theory is correct, that God's existence is compared to an infinite time line, then at the point in time that I picked up the pen, God was with me in the room— at the same point in time that I was. Not only does this idea make God seem more vulnerable and human-like, but when He is at the point on this line that I picked up the pen, He is not at any other point on the line. How is He to know whether or not I will pick up the pen if He is only at the current point in time? We have already said that God DOES know that I will pick up the pen, but with your theory how is He to know?!
Because of the problems listed, I appears to me, that God existence can not be compared to an infinite time line. I believe God is living above time all together. He is so infinite, His existence doesn't have the word time in it at all. Time is ABSOLUTELY NOTHING to Him. Therefore He can not live on an infinite TIME line. He is living in an area or "universe," if you will, that is not affected by time. He has no beginning or end, rather he just... is. Imagine the history time line in your head. You see the beginning of the Earth on the left, and Masiach at the end, on your right. Where is God on this time line? He isn't. Rather he is living above it, not bound by time at all but rather is just existing. He understands the rules of time— he has created it— but does not live by them. He knows what you will do because he is at every point in time, all at the same time. He was, He is and He will be, not at separate points in time, but at the same time! He doesn't exist like we do. When people die, they don't wait until they are resurrected, rather they are like God, I think, in the sense that they are living in an "alternative universe" where they just... are.
To answer your question, it isn't that history is an infinite line, where we could be placed anywhere. It is merely a finite line, and God lives separately. Therefore the line of history isn't infinitely long, but rather only 5000 years long. The chances, therefore, that we were born when we were are infinitely less then what you suggested.
(Considering your theory was correct...) God isn't bound by percentage. You can not say that because there is a 0% chance of being placed where we were we can not be placed there. God is infinite and can do infinite things. So even if there was a 0% chance, that doesn't affect God. Imagine God deciding to place me in year 2016 and then an idea called 0% saying, "Um, no, You can't do that."