Nope
2-dimensional space is composed of several 1-dimensional spaces layered on top of each other. 3-dimensional space is composed of several 2-dimensional spaces layered on top of each other. A 2-dimensional being cannot see anything beyond their own 2 dimensions, because the 2-dimensional plane on which they exist is the entirety of their known world; they exist in their own 2-dimensional space, and that's that. They cannot conceptualize three dimensions because as far as they know, their 2-dimensional plane is everything, and how can there be more layers of everything?
Similarly, our three dimensional world is everything as far as we can perceive. 4-dimensional space would involve more 3-dimensional spaces stacked on top of each other, but as far as we can tell, it's impossible to do that, just like it's impossible to create 3-dimensional space for a 2-dimensional being. It is impossible to visually depict 3 dimensions within a 2-dimensional world because the 2-dimensional world lacks the third dimension that would be required. Similarly, it is impossible to visually depict 4 dimensions within a 3-dimensional world.
You should find and read a book called Flatland, by Edwin Abbott Abbott. In it he rather effectively describes what would happen if you tried to introduce a 2-dimensional being to the third dimension. I think it will give you the insight you're looking for.