Question: Is it possible that the universe does have a center after all, but we just cannot see it because it already fell beyond the event horizon of our observable universe?
If not, how do we know this for sure if we cannot observe it?

Answer: 
Science is all about predictive power. It is entirely possible that the laws of physics are completely different from the ones we know. The universe could be managed by tiny deamons and are just waiting for someone to sound a trumpet before the walls come down. However, there's no evidence to suggest we can make predictions in this way.

What we can say is that every observation we have made is consistent with the universe having no center. If we make predictions based on this assumption, we have a curious tendency to be right.

There's nothing that prevents there from being a "center" elsewhere, if the laws of physics still resulted in the same set of observations that we see. We tend to ignore this because the results are more complicated, and they don't provide any better predictions.

To borrow from Russel's Teapot, I can predict that balls fly through the air in a (roughly) parabolic arc. I can also predict that balls fly through the air in a parabolic arc and there is a teapot orbiting around Jupiter. Unless I can make observations around Jupiter, the second theory doesn't add any more predictive capability, so we can side step it entirely.

In the case of the idea that the universe has no center, we can stick to that simplistic notation until someone finds out how to observe something outside of the observable universe. Obviously this phrasing has some drawbacks...
There are things we can observe with great precision which furnish evidence that your scenario is incorrect, as follows.

If it were true that the universe has an expansion center, then the part of the universe we inhabit would look different to us in different directions: we would see younger structures in one direction (toward the center) and older structures in the opposite direction (away from the center). This is not observed.

In addition, the younger structures toward the center would have their spectra red-shifted less and the older structures away from that center would be red-shifted more. This is not observed.

In addition, the cosmic microwave background would be strongly anisotropic in a manner that matched the spectral shifts. This is not observed either.