No. To humans the fourth dimension is incomprehensible, and we only see evidence of it when studying the universe. Space is somehow curved in another dimension, yet there is no way any of us will ever "see" it.
Imagine a two-dimensional world. People live in the flat world and they are only aware of their own flat landscape, and they can't see anything out of their dimension. Now imagine something 3-dimensional like an apple passing through their flat world. They will only be able to see a cross-section of that apple at any time, and they can't grasp the concept of the full apple, and never will be able to see the whole apple.
The apple is still there, and the people in flat land can see glimpses of it and they know it's there, yet they can't comprehend what the third dimension is...they only see shadows of it. Our concept of the fourth dimension is very similar---we know it's there, and we can see shadows of it, yet we can't see the true fourth dimension.