Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be movement in water which will tell us that the ball underwent motion. But since we have nothing to compare the motion with how can we say that it was in motion? can we say that it was at point A inertially (in space) and then in point B (again in the empty space)?
I don't know if you came with this thought experiment by yourself but if you did you are crazy smart. This is actually very close to the argument made by Newton, usually called Newton's Bucket. He believed that absolute space was a real physical scenario where physical processes were to happen. And something similar to that is his main argument for it's existence.
The truth is that today we don't consider this to be empirical evidence for that idea necessarily. To join a concept of relative space been the only one in existence with the results of this thought experiment you can just suppose that the objects of the rest of the universe are somehow mysteriously influencing the water communicating it what its movement relative to other objects is. In the extreme case were only your ball filled with water exists the believe is that water would actually not slosh at all. This is calles Mach's principle.
Today with the Einsteinian view we think in another way. Space is nothing more than a conceptual construct, an abstract aid for calculations, but space-time is something physically real and something entirely different.
You are asking if we can take space as a universal reference frame. Now what we usually use as universal reference frame, is the CMB. But in SR and GR, there is no universal frame of reference in theory.
But let's disregard that, and say you want to move that bucket with water.
First of all, how would you say if the bucket was in motion (constant speed) in the first place? In an empty universe you could not tell (about constant speed).
Speed is relative. You need to specify what your speed is relative to. In your case, in an empty universe, there is nothing to compare it to.
Now if you want to move the bucket what you really do is you accelerate it (at least for a while). Now acceleration is absolute.
Even in an empty universe, you are able to tell if your bucket accelerates or not. First, as you say, the water will move differently from the bucket because of the acceleration.
But, you can also drop beacons from the bucket as it accelerates. With a laser, you can check the distance between the following beacons, and you will see that this distance increases with each new pair of beacons. Thus, the bucket is accelerating, and you can tell even in an otherwise empty universe.