Even if interstellar voyagers in our galaxy maxed out their velocity at 0.01c, they would still need less than a 1% head start on earth to cover the entire galaxy. Yes, we do not have technology to do this now. Less than 100 years ago we did not have technology to send an object into orbit. It's conceiveable that our space travel technology will continue to improve. How advanced do you think human space travel will be in a million years? Say it takes us a million years to achieve interstellar travel at 0.01c. That literally does not change the result of the above calculation. I don't know why some here are adamant that interstellar travel will never happen.
The difference in opinion is whether technological advances are just a matter of time, or if there are physical limits that we know about today that will never be overcome, no matter how much time is available.
My personal opinion is that there might be potential for learning new, even unexpected things that would allow us to do in the future what we think is impossible today. So, I am in the "never say never" camp on the
possibility.
On the other hand, when it comes to making an
objective assessment of the Drake Equation, about why we are not seeing a thriving interstellar travel community in a billions of years old universe, my opinion is that we do have to consider that it might be impossible, no matter how much we learn.
Or, maybe there really just isn't anybody else out there. There are plenty of "ors" in the currently possible interpretations of that equation with the current state of our knowledge.