I think you could actually break this down into two questions:
1. Does God change with time?
No, the Bible seems to say that God is eternal and unchanging. In Malachi 3:6, God says, “I am the Lord, and I do not change.” (NLT). Abraham and Moses both refer to God as the “eternal” god (Gen. 21:33, Deut. 33: 27), and Paul certainly picks up that theme in Romans 1:20 where he refers to God’s “eternal power.”
However, I think a good second question would be:
2. Does our relationship with God change over time?
In this case, emphatically yes! Paul says in Gal. 3: 24-25, “The law was our guardian and teacher to lead us until Christ came. So now, through faith in Christ, we are made right with God. But now that faith in Christ has come, we no longer need the law as our guardian.” (NLT)
A pretty scandalous statement for a Pharisee and expert in the Law of Moses to make!
Paul seems to suggest that the Torah or Law in the Old Testament (with all of its guidelines about what to eat, what to wear, how to relate with people, etc.) was given to the Jewish people (and incidentally to the world) for a time as a way to show us what is right and wrong; as a way to show us what God wants us to do.
But now Paul seems to say that we have changed. We have grown up, so to speak. For a time, the law was given to us to act like a guardian or a babysitter; telling us when to go to sleep, don’t eat too much candy, etc. But now, because we can place our faith in Christ, we no longer need the law as our guardian.
Paul seems to suggest that in Christ, we mature in our faith, and living out love as Jesus teaches will actually fulfill all of the requirements of the law. (Matt. 22: 34-40)
Love will now allow us to maturely live out the principles that were given to us in the law.
When we are 5 years old, we need to be told when to go to bed. We need to be told don’t eat too much chocolate or we’ll be sick. We need that sort of guidance at that age. However, try telling a 20-year old when to go to bed!
Hopefully by 20 years of age, we’ve learned why it’s healthy to get a lot of sleep, and we don’t need to be told when to go to bed. In fact, if we try to live by the same rules at the age of 20 as we did when we were 5, it will actually be harmful to us and to others!
Now, if you are the parent of a child such as this, and you change how you relate to your child, does that mean you have necessarily changed? Certainly not! But your relationship with your child has changed because time has passed and they have grown.
This is what the Bible seems to suggest has happened in our own spirituality.
In the Bible, we have an Old Testament and a New Testament. We have an old way of relating to God and a new way of relating to God. We have an old way of living by religious rules and regulations, and a new way of living by the principle of love that Christ teaches.
But the eternal, unchanging God is the same parent behind both ways of relating.