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: 
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.
The universe [doesn't have a center](https://www.livescience.com/62547-what-is-center-of-universe.html), so this question is not well-posed.

If your question is "can the universe have a center anyway?" then you would be challenging the Big Bang, which is something that (as of 2021) is very much in the fringe.