> Catholicism teaches that Divine Revelation is God's Self-Revelation and therefore can't change because God can't change.

The "God can't change" part seems a bit above our paygrade, no?

Not to mention: Who are we to say that God wouldn't reveal things to us gradually — and maybe in a changing way?

EXAMPLE: We still teach our kids that the sun rises in the east and sets in the west. Later, we refine the teachings.

This misunderstands the theology and metaphysics very profoundly.

The immutability of God is a necessary theological conclusion. If God changes, then He isn't God, by definition. It would be a metaphysical absurdity. Change presupposes imperfection and, therefore the potential for perfection, i.e., full actualization, but God as the Ipsum Esse Subsistens, is pure act with no potential left to actualize. God is fully dynamic, but this is quite different from change. He may appear to change from our temporal perspective as events are distributed in time, but from an eternal perspective, all is actualized, "simultaneous", so to speak.

W.r.t. gradual revelation, that is exactly what Scripture is a record of. A Catholic reading will demonstrate that revelation is in the business of slowly revealing to Man who God is (at least that which cannot be known through unaided reason; quite a bit can be known through reason alone), preparing him for the culmination of public revelation in the Incarnation of the Logos, something foreshadowed in the Old Testament. And furthermore, the Catholic Church recognizes the development of doctrine, which you could call a refinement and deepening of understanding of what has been revealed. I like the analogy to mathematics, even if it is imperfect: all the theorems that follow from a set of axioms are in a sense already in the axioms, and so mathematics is in the business of unpacking them.

However, this gradual revelation and development of doctrine, in order to be authentic, cannot contradict what was known previously, at least to a certain accuracy, if not precision. Of course, here is where people can get tripped up by analogical devices and literal-mindedness. Scripture is written using the idioms, paradigms, and language of the people who wrote it and for whom it was written. That means that some of the language may not agree with strict scientific descriptions of the 21st century. However, when that does occur, you will note that the sense is not the reference: when the Bible speaks of the sun rising in the east and setting in the west in order to communicate some theological truth, it is not making astronomical claims about the sun and the earth. It is using this language as instruments to communicate something, often by analogy. In fact, analogy is essential to theology, something captured in the concept of the analogia entis. Univocal or equivocal approaches to the subject of God have been the source of numerous heresies.