If something lasts long enough we see it as a real object. Something that is beyond time and space could only be what senses and relates to it. The next "dimension" will be we call ascension for those able to understand it, I believe. Some would call it the astral world or dream state. It requires a higher level of being.
In the context of what you're saying (which isn't the context of the speed at which our eyes can see), you can't technically see anything "that lasts long enough" because you imply that it needs to have "linear time" in order to be visible.
We can only "see" what is in the "present". We can never "see" what is in the "past" or "future" in the sense that you are talking about.
So that 3d cube marked "present" is the ONLY thing we can see given standard circumstances.
Another note is that we only "see" in 2D, not 3D. In order to "see" in 3D, you must be able to perceive whatever is at all 3 coordinates of 3D at the same time, which means if you look at me in 3D you must be able to see my heart pumping, inside my chest with your very own eyes without opening my chest with a knife. But the fact is, we only see x,y (how tall and how wide). We can't see the "depth" otherwise we'd see THROUGH everything too (a surface (i.e 2D area) won't block our vision).
Our perception of "depth" is actually two 2D Maps from each eye interpreted by our brain to ONLY tell us "how far" a point is on that 2D map from us. It can't necessarily tell us "what exactly is at that point of depth", because it might be inside an opaque object that our 2D-viewing eyes can't penetrate.
Its sad to say but we can only see in 2D if we're talking eye-sight.
Another thing I want to point out is that the term "dimensions" imply the addition of "planes" as reference points. where 2D has "2" dimensions x,y and 3D has "3" dimensions x,y,z we think that there's a 4-dimensional way of perceiving something directly with 4 dimensions x,y,z,+1
But look at that dimensional diagram. See how each "higher" dimension is actually just the previous one in "stacks" or in "series". A whole bunch of 1-dimensional lines next to each other will look like a 2-dimensional square(area). A stack of areas on top of each other look like a "cube".
In the end, its not really 3 types of dimensions, its still "one" type of dimension. It is a coordinate, a point. Each "higher" dimension is just another set of points. But only space works like that. Time does not. Otherwise I can just take a 3-d cube on my desk, move it with my hand to the other end of the desk, and say "hey look at my 4d hypercube moving through past and present and future". I'll get laughed at because its still a 3-d cube, its coordinates just changed, and its 5 seconds later in the day. Nothing impressive about it. It didn't "ascend" and became a "4-D hypercube" by the "divine might of so-so" moving his "mighty arm of godlike powers through time and space" just because added some linear attribute to the cube. Ahem...
Time works in cycles (e.g. vibrations, patterns), duration (persistence), transformation (change in "substance"), intensity (intensity we could inaccurately understand as "speed" or "energy") and such attributes that we can't explain with spatial coordinates called points.
4-D hypercubes are thus not "3d plus time = 4D". Its still 3D, with a linear relativity (backwards and forwards) and a direction (e.g. past is backwards, future is forwards) as additional attributes. Think of those attributes as the "color" of the cube and the "brightness" of the cube. color and brightness are just additional attributes of the same 3d object. They don't make the object 5d simply because its got color AND brightness in addition to 3 dimensions of space.
If you want to think of a 4-d cube, think of a spinning 3-d cube. want a 5-d cube? Make it change between variations of matter, anti-matter, and vacuum as its "substance" while spinning for only a duration. want a 6-d cube? Have it in a pattern of absorbing and radiating energy as it spins and changes in substance all at the same time.
This doesn't make sense. There's a reason for that. Because its not stable, not useful, not sustainable. Everything that exists in some form of sustainable state (i.e. for longer than some instant of linear time), doesn't exhibit an x+n amount of dimensions. It exhibits a precise, limited amount of dimensions. The dimensions are also not described with one type of coordinate, but different types of coordinates.
"Ascension" is not the 'addition' of dimensions, it is the awareness of more types of coordinates of the already existing dimensions.
Now some may say "but they have proven 10 or 12 or x amount of dimensions with math". What type of math? Did you know there's at least 9 types of math? And that they are not compatible with each other - thats why they're distinguished from each other. And why should "reality" subscribe to a man-made type of "math" simply because that "math" says it must?