The concept of galaxies that are billions of light years away despite the finite age of the universe can be explained by the expansion of space. This phenomenon is known as cosmic expansion or the expansion of the universe.
According to our current understanding of cosmology, the universe began with the Big Bang approximately 13.8 billion years ago. Since then, the universe has been expanding. As space expands, it carries galaxies along with it, causing them to move away from each other. The farther away a galaxy is from us, the more the expansion of space has stretched the light emitted from that galaxy.
When we observe distant galaxies, we are effectively looking back in time because the light from those galaxies takes time to reach us. The light we receive from a galaxy that is, say, 10 billion light years away, was emitted when the universe was much younger. During the time it took for that light to reach us, the universe continued to expand, causing the galaxy to move even farther away.
In this way, galaxies that are billions of light years away are remnants of the early universe, and their light has traveled across vast distances to reach us. The expansion of space allows light from these distant galaxies to reach us, even though the age of the universe is finite.
It's worth noting that the expansion of space is not limited by the speed of light. While information and objects within space are bound by the speed of light, the fabric of space itself can expand at rates greater than the speed of light. This is possible because the expansion of space itself is not subject to the same restrictions as objects within space.