The first thing to be said is that the importance or value of something is not always, or even usually, determined by its physical dimensions. Our most treasured possession is not necessarily the largest thing we own. And who would deny that a single human life is more important than an entire galaxy that was devoid of life?
The second thing to be said is that far from pointing to our insignificance, the vast size of the universe is actually a precondition for our being here! The reason is that if the universe were much smaller than the billions of light years across that we observe it to be it would not have lasted long enough for complex living things to have evolved.
First of all, before any life could arise, the chemical elements had to form. Most of the chemical elements needed for life were produced in the hot interiors of stars by nuclear reactions that fused together smaller nuclei, starting with hydrogen and helium, to form larger ones, such as carbon, nitrogen, and oxygen. When such stars exploded as “supernovas,” they spewed those elements out into space, where they eventually formed new stars and new planets (like the Earth) that possessed the chemical elements needed for life. These astrophysical processes required billions of years to unfold. And that was just the beginning. The next stages were for life to form from those elements and then evolve from one-celled organisms to complex multi-celled creatures such as ourselves. And we know this also required billions of years. So, certainly, the vast age of the universe is a precondition for us to be here.
But that means also that the vast size of the universe is a precondition for our existence, because the laws of gravity discovered by Einstein relate the size of the universe to how long it lasts. For a universe to last the billions of years needed for complex life to arise, it must reach a size of at least billions of light-years across. Suppose, instead, that the universe never got larger than a “reasonable human scale,” say a few thousand kilometers across. Then, according to the equations of gravity, the universe would last for only a fraction of a second --- that is how long it would take for it to expand from the Big Bang to a maximum size and then re-collapse to a final “Big Crunch.”
There is a final point to be made. According to Christian teaching, the universe was created to manifest God’s glory. (See sections 293-4 of the Catechism of the Catholic Church.) “The heavens declare the glory of God,” says Psalm 19. A famous medieval theologian, Cardinal Nicholas of Cusa, speculated that the universe might be infinite in size, because that would, as he saw it, most fittingly reflect God’s majesty. He even speculated that there are an infinite number of other heavenly bodies and that an infinite number of them are inhabited by rational beings. It is certainly possible that it is part of God’s purpose that there be rational beings elsewhere in this universe. And the larger the universe, the more life it can contain. For further discussion of that issue see Question 15.
Resources for further study
Modern Physics and Ancient Faith, Stephen M Barr (University of Notre Dame Press, 2003) Chapter 13 (“Why is the Universe So Big?”)