I read from this link where some of the sentence is talking about God is always the same. Below is the verse quoted from that link :
You, Lord, in the beginning laid the foundation of the earth, And the heavens are the works of Your hands; They will perish, but You remain; And they all will become old like a garment, And like a mantle You will roll them up; Like a garment they will also be changed. But You are the same, And Your years will not come to an end
So I think from the point-of-view of the writer of the verse above is that if something become old then it's not the same anymore. In other words, in the writer's point of view is that God will not become old, hence he wrote : "But You are the same".
Assuming the writer is there also with the baby, Mary and Josef at the stable, and Mary say to the writer "this is The Lord you wrote about". Then after three years past, the writer see that the baby becomes old, will the writer's following argument valid ?
The Lord will not become old
This one become old
So, this one is not The Lord.