According to the LDS church, why was Jesus Christ born when he was born?

Why was Christ born when he was born? Why not earlier? Why not later? Does the time period of his life have a symbolic or practical importance? I am not aware of any reason why Christ needed to live when he did other than to fulfill prophecy, but that prophecy only exists because God had previously chosen the time for Christ's birth. So why? The reason for Christ's life was to perform the Atonement , but I can't imagine the particular timing of it mattered much since it was an infinite atonement . Another effect of the atonement is that it enabled missionary work in the spirit world as well as performing temple ordinances for them. Many spirits had to wait a few thousand years for this to happen. It seems like they might have preferred if Christ had lived earlier so that they didn't have to wait so long. One might say that time only exists on this earth and not in the world of spirits, so why then is genealogy and temple work so important? I'm willing to accept that the answer to my question is "because God said so" but I would like to know if there happens to be more than that.