As far as I know we are able through tests to just detect the degree of such a presence with no possibility of detecting the full extent.
Since Science is unable to measure and weigh such does it exist?
Would seem to me an untenable position to hold as a Scientist. Just to state precisely the exact position one is in while in a moving universe is so profound that as a scientist I would not seek any dogma that states what really is and what is not purely on the basis of whether it can be measured.
My last and only course in psychological testing was probably late 1970 or early 1971. That said, I'd personally be very uncomfortable predicting ultimate limits for a person above a certain level of brain development. (Say, the "basket-case" level.)
One problem with trying to quantify creativity issues, there are a lot of "eye-of-the-beholder" issues. A kid makes a finger-painting. I see smears; you see a masterpiece. Is the kid creative? Depends who gets asked.
Since Science is unable to measure and weigh such does it exist?
Depends on your definition. The human brain, anyone's, is a finite thing. But can you imagine all the things that could come out of that brain in any situation? No. The brain responds to the environment, and if you're leaving the potential environmental stimuli unbounded, you can't put a bound on what might come out of the brain. Anyway, that's my best guess.
Quantifiability is important to a science's claim to be science, which is why Psychology has been striving for it for many decades. It wants to become a "hard science" instead of the squishy soft thing that it still is. (I'm being generous here. In other moments, I've agreed with a character on the old Newhart show that "it's all a crock.")
(There is a down side to this rush to numbers in that various scores and indexes are trumpeted as meaningful only to have subsequent studies undermine or qualify their reliability. How many people on this forum have bragged up their IQ or their SAT scores as if they were some kind of rock-solid achievement?)
Let's look at the converse of your statement:
The "real science" has to include things that can't be measured or quantified. (Or even detected, as Betty Boop sometimes suggests?)What's real about that science? How do you check to see if it's right?