Based on our current understanding of the universe, it is not possible for our galaxy, the Milky Way, to leave the observable universe. The observable universe is the portion of the universe from which light has had enough time to reach us since the Big Bang, given the finite speed of light.
The observable universe is vast, extending over 93 billion light-years in diameter. Any object or region within the observable universe is in principle visible to us, given sufficient time for light to reach us. However, due to the expansion of the universe, the observable universe is also continuously growing. The expansion of space causes distant objects to move away from us, resulting in an ever-increasing observable universe.
While galaxies, including the Milky Way, are moving away from each other as the universe expands, the expansion itself does not cause galaxies to leave the observable universe. Rather, the expansion stretches the space between galaxies, causing their recession. It's important to note that the expansion of space is happening uniformly throughout the universe, affecting all objects within it.
Therefore, as long as the fundamental properties and mechanisms governing the universe remain consistent, our galaxy will always be within the bounds of the observable universe. However, it's worth noting that our understanding of the universe is continually evolving, and future discoveries and advancements in our knowledge could potentially shed new light on this topic.