While it WAS thought that the human race is about 200,000 years old, they found a human footprint a few days ago that may be as much as two million years old – tests are ongoing.
While there are certainly many incorrect answers to your question, I’m not sure there is a “correct” answer. But here is my answer.
If you subscribe to the theory that God used evolution as a tool to create Man, as I do, then the more important act of creation was when God breathed an immortal soul into Adam – not how or when the human race developed into homo sapiens.
So in my mind, your question becomes: as the first “humans” were evolving until finally the homo sapiens arrived, why did God wait until Adam to breathe eternal life into his creation? I think the answer is the same for your question as well.
It is because God had to nurture his new creation until homo sapiens were sophisticated enough and mature enough to enter into a relationship with Him. God first attempted to enter into a relationship with Adam, but the Fall of Man caused some problems there which ultimately led to the Great Flood. The next major involvement was with Abraham, Isaac, and Jacob (not Moses as you mentioned). Why the long wait from the Fall until Abraham? Again, I think He had to wait until Man was sophisticated enough to be able to enter into a Covenant relationship with Him.
Skipping the remainder of the Old Testament, your next question is: why did God wait so long to give us the opportunity of redemption through Jesus Christ? Again, I think He had to wait until Man was mature enough to understand the nature of love – to understand God’s love for us as shown through the sacrifice of His Son, mature enough to accept this love, to love and respect ourselves and our fellow man, to love God for himself – not just for what He does for us, etc.
So in each case, the answer to “why did God wait so long to do this or that” becomes "because he had to wait for Man to grow up, to become sophisticated in his relationships with his fellow man and with “the divine,” to become responsible enough to understand honor and promises and the nature of a Covenant, to understand love in all its varieties and to be able to love God as he should be loved.
I hope this is helpful.