To explore the entire universe or even our Milky Way galaxy would require leaps in technology that we can't yet fully anticipate. The speed of light sets fundamental limitations on how fast we can travel and how much of the universe we can explore within a certain timeframe. The distances between galaxies are so vast that even with theoretical propulsion systems like nuclear propulsion or concepts like the warp drive (based on theoretical physics), reaching distant galaxies would take an incredibly long time.
Additionally, the universe is continually expanding, and its ultimate size and structure are still subjects of ongoing research and debate in cosmology. The concept of reaching a point where there is no more exploration left to do is complex, as new discoveries can always be made, and our understanding of the universe is continually evolving.
It is possible that as technology advances and future generations build upon our current knowledge, exploration capabilities may expand, allowing for more extensive exploration of the universe. However, it is uncertain when or if we will ever reach a point where we can claim to have explored the entire universe or galaxy in its entirety.
In summary, while humanity's curiosity and drive for exploration are likely to continue, the complete exploration of the universe or our galaxy is currently beyond our reach, and it remains uncertain whether it will ever be fully achieved. The journey of exploration is an ongoing and dynamic process, with new discoveries waiting to be made at every step of the way.