The concept you've presented, where the universe began 13.8 billion years ago and is now infinite, might seem paradoxical or counterintuitive at first glance. However, it's important to clarify a few points that help reconcile this apparent discrepancy:
Universe Expansion: The Big Bang theory, supported by substantial observational evidence, suggests that the universe originated from a highly dense and hot state approximately 13.8 billion years ago. Since then, the universe has been expanding. The expansion of the universe doesn't imply that it started from a single point and expanded into a preexisting space, but rather that space itself is expanding. As the universe expands, distances between objects increase, leading to the observed phenomenon of galaxies moving away from one another. The expansion of the universe is ongoing, and it does not require the universe to be finite or infinite.
Infinite Universe: When scientists discuss the possibility of an infinite universe, they generally refer to the spatial extent of the universe. In an infinite universe, there would be no bounds or boundaries, and it would extend infinitely in all directions. This concept doesn't contradict the idea that the universe had a beginning or originated from a highly dense state. The infinite spatial extent refers to how the universe is currently, not necessarily how it was at its inception.
Cosmic Inflation: The theory of cosmic inflation proposes that in the early stages of the universe, there was a rapid expansion, causing the universe to become much larger than its observable region. This inflationary period would account for the vastness and homogeneity of the observable universe. However, it's important to note that the concept of cosmic inflation does not require an infinite universe.
In summary, the universe began with the Big Bang approximately 13.8 billion years ago, and since then, it has been expanding. The term "infinite" when applied to the universe generally refers to its spatial extent, not the notion of coming from non-existence to infinity within a finite time. The concepts of an expanding universe and the possibility of an infinite universe can coexist without contradiction.