"My soul languishes for thy salvation; I hope in thy word.We're over two thousand years separated from the event. We can't see Jesus being born. Yet two thousand years ago, there were no witnesses either, save for the Blessed Mother and St. Joseph - none other save for a few barnyard animals. Being apart from it, whether by space or time, doesn't change the importance or impact of His birth on each of us.
My eyes fail with watching for thy promise; I ask, "When wilt thou comfort me?"
For I have become like a wineskin in the smoke, yet I have not forgotten thy statutes.
How long must thy servant endure?" (Psalm 119:81-84a RSV)
Our God is not bound by time. The sacrifice of Christ becomes present to us at every Mass , Jesus' perfect offering washing our sins as surely as if we were there at the foot of the cross. Indeed, at each Mass we are are the foot of the cross. For our God, unbound by time, every moment is present. Christ's birth is as present, as real, today as it was millenia ago. We, as His Body, "the Church never tires of singing the glory of this night." 
Truly, on this night, our wait is over and our Savior comes.