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: 
We cannot know “for sure” that the universe beyond the observable universe is the same as the part of the universe that we can observe. But “for sure” is not a benchmark that science tries to achieve (or, indeed, can achieve).

The principle of [Occam’s razor](https://en.wikipedia.org/wiki/Occam%27s_razor) tells us that if we can think of several possible explanations for observable facts, we should favour the one with the fewest untestable assumptions. In this case, a cosmological model in which the universe expands uniformly in all directions and has no unique centre is better than one that assumes a centre of expansion that is so far away we can never observe it or detect any evidence of it.
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.