One has to define the terms one is using.
means a stationary point, an unchanging point
In physics, motion is relative. One can define the earth as stationary, then everything else is moving around the earth in complicated mathematical functions. The simplest planetary model is to take the center of mass of the sun and the planets, then every planet and the sun are moving around the center of mass in simpler mathematical functions. We could consider that as a static center of the solar system, by defining it as such. But the solar system is moving with respect to the galaxy, the galaxy is moving with respect to the center of the galactic cluster. If we take any cosmological group, clusters of galaxies for example, we could define a center of mass. When we come to be talking of the Universe though, we need a mathematical model further than simple Newtonian gravity to fit the astronomical observations, and that is General Relativity. It fits the observation of clusters receding from each other and the data of cosmic microwave background radiation.
The center of the universe can be a reference point if we consider a three dimensional space.
The astronomical observations are incompatible with a three dimensional universe in space. General Relativity involves a four dimensional space-time that has the universe evolving from a singularity ( a single point that is undefined in space and time) from what is called the Big Bang and every single point in our space now has evolved from that single point of the singularity, almost forteen billion years ago. Thus the concept of a center in space has no meaning in the accepted and validated with observations cosmological model.
After the edit of the question:
In 1929, Edwin Hubble confirmed that the Universe is expanding (consider that with respect to that reference point).
That and the validation of General Relativity by other observations also, makes GR the mathematical model of the four dimensional universe.
Does that imply that we cannot have a single static four dimensional point (i.e., space and time changes ever) in the Universe?
We do have a single static four dimensional point, the singularity from which the Big Bang started. (it is always x=0, y=0,z=0,t=0)