The concept of a "center" of the universe can be a bit tricky to define within the framework of our current understanding of cosmology. According to the Big Bang theory, the universe began from an extremely hot and dense state approximately 13.8 billion years ago. However, it's important to note that the Big Bang did not occur at a specific point in space, but rather, it was an expansion of space itself.
The universe does not have a well-defined center that we can pinpoint. Instead, the expansion of space that occurred during the Big Bang happened uniformly in all directions. From our perspective, it appears as though galaxies are moving away from us in every direction, giving rise to the concept of an expanding universe. However, it's important to note that this expansion is happening at every point in space and not just from a single central location.
Regarding our solar system and galaxy, the Milky Way, they are part of the larger structure of the universe. The Milky Way is a barred spiral galaxy, and our solar system is located within one of its spiral arms. However, the Milky Way is just one of countless galaxies in the observable universe, and it is not at the center of the universe either.
In summary, the universe does not have a definitive center that can be identified based on our current understanding of cosmology, and our solar system is located within the Milky Way galaxy, which itself is part of the vast structure of the universe.