Except that tree rings are formed
only because of one process: when a growing tree is exposed to seasonal changes in weather (wet/dry, cold/hot). The formation of rings is so precise that rings of trees in the same region (exposed to same weather), even those of different species, can be matched ring to ring because their growth rate is the same.
Now, when God creates a tree ex-nihilo, there is no need to put those
growth rings there for the simple reason that the tree
did not experience any growth. In other words,
the trees have rings because they experienced growth, not because they are old. Age has nothing to do with it, history does. It just so happens that history of growth correlates very well (99.999%) with age since there is only one growth season per year. So we calculate the age from the history.
If your "embedded age" idea were correct, we should be able to count back to 4,000 in tree rings and the trail would stop there. Unfortunately for embedded age, that is not the case as in nature we find broken lines of rings going back at least 10,000 years.
Here an interesting article from a source that I think you should find reliable:
Are tree-ring chronologies reliable?