The limit to space travel is the Rocket Equation, which says that you require exponential fuel to reach higher speeds. Alpha Centauri isn't going anywhere, but it will take millennia of travel even with wildly optimistic assumptions.
Also note that there isn't any "container" to fill up. It could well be infinite. It's just that we will be forever limited to a finite subset, even in theory.
There are theoretical designs using antimatter (pion rockets, or beam core engines) that could reach 0.4c - 0.7c, which puts Alpha Centauri at decades away, not millennia.
Also note that there isn't any "container" to fill up. It could well be infinite. It's just that we will be forever limited to a finite subset, even in theory.