Alright, bare with me...I'm going to try and explain my thought process before I dive into the question!
Who says a soul is something that can be explained through technology, thought processes, and knowledge we have today? It's natural for you to believe we don't have a soul because all your points are based on only what is known "today". Yes I know that's how we all make logical conclusions...based on "facts" and what is known today and not tomorrow....You know the run down sayings "They used to believe the earth was flat" or "The planets and stars revolve around the earth"...Those at the time were based on their truths through science. Of course today we laugh because we know the earth is pretty much a sphere...or is it

? I joke....anyway, that's my thought process on that.
The main reason why from a scientific perspective souls aren't believed to exist is because there is no evidence of their existence. The concept is not strictly IMPOSSIBLE, just improbable considering souls do not pertain to any measurable matter or energy change in state. Supposedly after we die our soul leaves our body, yet such a change in state between life and death has no particularly measurable consequences in terms of a soul. There is no reason to believe if there is no observable evidence to suggest existence.
In regards to a true scientific perspective, every viewpoint is subject to scrutiny and change. If there was an irrefutable test for the existence of a soul, and it was completely and entirely repeatable with similar results each time, then it would turn in to a cold, hard fact.
I'm a pretty open and abstract thinker pretty much on all fronts. I like to play devils advocate so here I go haha.
I believe the brain is in control of our physical self. A physical self one can see, feel and examine! However we exist in the forth dimension but only see three of them? Now I'm not saying souls exist in the forth dimension because time is that forth dimension. Its such an abstract thing to think about, but we know its there, its around us 24/7 (literally lol) yet to fathom its actual existence is mind boggling. As I'm typing this I'm trying to get a grasp on even just the thought of being able to see it. And honestly it kind of just scrambles my brain haha. That being said.........there are still many other dimensions THAT WE KNOW OF...and who knows probably others we don't
I think you've misconstrued what a dimension actually is. You don't APPARENTLY see time as your eyes are receptors of light. However we know that light has velocity. You see things from the light that enters your eyes, that originated from something a very short amount of time beforehand. So technically, while you don't experience time with your eyes per se, it is still very much perceivable if you alter your perception a little. Look in to the theory of relativity if you're interested.
I'm not really comprehending where this connects to having a soul, though. Are you suggesting a soul can exist in another dimensional plane or curve? So can we, actually. This reminds me of that Doctor Who episode "Go Left" where Donna goes right instead of left and creates an entirely separate timeline. Timelines are, I would dare theorise, curves in the fourth (possibly fifth) dimension, so our choices affect how we traverse these dimensions, just like how we can choose to walk forward or drive a car to traverse the first, second and third dimensions. Nevertheless, this is speculative at best (I'm not exactly a specialist in metaphysical phenomena) and still doesn't really connect to the concept of a soul.
Just because you cannot perceive it does not mean it isn't there!
Side note: I don't think of things in their traditional sense. When I think soul I do not immediately associate it with religion in anyway. A word is just a word and that's all that it is for me. I try not to get wrapped up in it.
As I mentioned earlier, you may not "see" something, but you can perceive it.