“Genuinely mathematically infinite - or just a really, really large amount expressed via hyperbole?” It’s the latter, because “the yearning for the infinite” is correlated with our subjectivity; when we conceive mathematical infinity, we don’t “yearn for it” like poets do when they contemplate the stars or human love. As finite beings, we can only imagine (and wish for) a multidimensional perception of reality, where the limitations of our body and mind don’t exist anymore and all things can be perceived simultaneously instead of successively. We don’t like the fact that we are finite beings, with a limited knowledge about the universe, with a language that can only express reality in terms of time and space, so we try again and again to overcome these limitations.
This is how the very ideas about God have evolved. The divine was described in concrete terms (multiple gods associated with various animals or birds, a family of highly anthropomorphized gods or an ethnic God represented as a monarch who defeats the gods of other nations, according to the social experience of ancient peoples), just like heaven or hell were described in concrete terms (actual places above the sky or under the surface of the earth, where souls enjoy the company of 72 virgins etc. or are tortured by fire or pitchforks).
But since we know that God is the source of everything and that by the Incarnation of Jesus we became entitled to call Him “Abba”, Father, we are free to see the old metaphor of the monarch as just one metaphor among many others. In the Catholic Litany of the Name of Jesus, we call Him “Sun of Justice”; G. F. Händel has a hymn known as “Jesus, Sun of Life”. These are not references to the pagan cult of the sun, but beautiful, poetic representations of the divine understood as the perpetual source of life and goodness.
So the ultimate source of joy can be called “joy”, the ultimate source of love can be called “love”, the ultimate source of light and life can be called “sun”, with the perfect awareness that we can’t actually comprehend and describe God like we can describe a physical object, but also with the perfect awareness that our poetic intuitions are correct, because we can recognize God in and by His creation, in and by humans and human creations. We know that God is not an old, bearded man sitting on the clouds. Likewise, the Church avoids any description of heaven or hell and emphasizes that any descriptions in terms of space and time are to be understood as metaphors.