Its a Paradox not a problem, therefore there is no "solution". This doesn't mean the chance is zero to encountering any other sentient race (or vice versa), only that the chance diminishes every day (just like finding Bitcoin blocks
)
"This" universe is known to be expanding, so yeah. Something "might" be there, but by the time we would reach it, they would be long extinct (or viceversa). We know most of the inner planets of this system will disappear in a few billion years. How long do you think it takes to go from place a to place b in space? A LOT.
Even if FTL travel gets invented, you still have a lot of problems. Simply moving from point A to point B, sets you in a different time flow, how many minutes you spend in point b does not correlate with the time flowing in point a, time dilation will effect greatly the father way you are, because... Everything in the universe is moving, not just generally expanding, but whole bunch of systems and galaxies rotating.
We are living in a outer edge of this known galaxy, which is rather out from the possible center. You do know that the edges rotate faster than the center, do you now? This means, our time is flowing already different. We are traveling "fast" compared to the center, so our minutes may be hours or months elsewhere. See where this is going yet? It gets worse.
This does not mean there could not be 1, 2 or 3; or multiverses or more. What exactly happens when we die, and where exactly do we come from when born? Is this life even life?
The truth is out there, or maybe not.
In the beginning (of the big bang) there was not even time flowing. So what was before it? and when is the expansion ever ending? Evidence suggests its just increasing.