The Catholic view of the universe is derived from divine revelation, theology, philosophy, and science, not only science. Science on its own is not the only way of looking at the universe.
Scientists would have to acknowledge that the structure of the universe is relative since science has shown that space and time are relative, that relativity itself is an essential characteristic of the universe. This is most obvious since Einstein’s theory of relativity.
For example, objects inside a moving car remain stationary relative to the inside of the car, which is objectively true but also relative to the inside of the car, whereas those objects are also moving at the same speed as the car down the highway, relative to a person standing on the side of the highway.
The organization of the universe is relative to the observer’s place in it. Therefore, a geocentric, flat Earth, and biblical structure exists right alongside a heliocentric, round Earth, and secular structure. Both are true at the same time, though the latter is secondary and subordinate to the former. This truth has eluded modern science and religious believers alike.
First, the Earth is both flat and spherical at the same time, but “flatness” is relative to human society observing the surface of the Earth. Practically speaking, the way we experience it as individuals, towns, and cities, it is flat in a practical way, and not curved. Likewise, from the view above the Earth, it is curved and spherical. Both are true, but what should matter to humanity is the relative viewpoint of humanity, therefore a flat Earth point of view.
Second, the Sun goes around the Earth, and the Earth around the Sun at the same time, but again relative to humanity on Earth. Relative to a certain part of Earth, let’s say Tulsa, Oklahoma, USA, at any given time the Sun is moving towards us in the morning and away from us at night. From the relative view of the Sun, Earth is moving around it, but both are true st the same time. This is not a purely subjective, psychological way of looking at the orientation of the Sun relative to the Earth, but an objective, scientific one based on the reality of relativity in the universe.
Likewise, the modern view of a vast, largely empty, expanding universe of galaxies, with our galaxy and solar system not being at its geometric center, originating from the Big bang, is still compatible with the biblical view. No where in the Bible, or Sacred Tradition, or magisterial interpretations of divine revelation, is the teaching that the Earth is literally at the center. Not literally. This is not in the Deposit of the Faith itself.
Rather, the “center” is a spiritual concept relative to living organisms that have a rational soul, and are made in the image and likeness of God. Therefore, morally and spiritually Earth is the center of the universe. This would be true even if there were on other planets living organisms designed with rational souls, such that the universe would also be organized around them as another “center” relative to their civilization.
By the way, this is why I have no problem or trouble in my faith with the idea that there may be other alien civilizations out there, or even with the possibility they here on Earth flying around in UFOs. They would still have the same triune God who made them, with their own history of creation and redemption.
Therefore, by holistically unifying the medieval and modern view, we still get a flat Earth, geocentric, and biblical view of the cosmos relative to human civilization living on the surface of the Earth looking upward. Above us is both a physical heaven and the spiritual heaven of angels and saints, that special place where God dwells in a sacred way looking down on us, ultimately bringing us vertically back to Him. He created the order of the suns, planets, and the moon to move relative to life on Earth in both a physical, material way, but also in a spiritual, harmonious way to reflect the order and harmony found in God Himself.
In conclusion, I think we believers need to engage our scientific world by showing it and ourselves that the modern scientific view can and must be reconciled with the medieval and Christian view.