It seems to me that when scientists can quantify something it becomes a dimension. It was by Counting on ten fingers that dimensions became possible. By counting days, and lunar months, and years, and adding a pendulum for minutes, Time was the first dimension. Then Length was measured by paces and cubits (one forearm) and inches (a bent thumb). By combining length and time you get the dimension of Speed. By measuring width, and multiplying length by width, Area also became a dimension. Add in a height measurement, and you get Volume. The invention of the balance made a dimension of Weight possible. By combining the dimensions of Length, Area, Volume, Time, and Weight, Newton was able to picture acceleration and the movements of the Solar System. Meanwhile Energy had been measured by horse power. Einstein managed to combine these basic dimensions in a unified model of the universe.
These days scientists also measure Color, Sound, Smell, Humidity, Pressure, and Pollution. I don't think they know how to measure Pain, Discomfort, Hunger, Curiosity, Sexual Feelings, Anger, Imagination, Anxiety, Joy, Love, Compassion, Thankfulness, Worship, Guilt. In the name of science some are trying to quantify measurable bodily reactions and the perceptions people give of these things.
I am not a scientist, and obviously that is a very simplistic impression of what scientists work with. But it seemed clear that anything which cannot be quantified is not science. It is on that basis that Modernity (the so called Enlightenment) divided our secular reality from religion which deals with values. In our postmodern world that division is no longer possible.
You are right that our universe and any parallel universe (such as the
world of our Creator) is bound to be infinitely more complex than the dimensions
scientists work with, and the experiences we can put into words. As Wittgenstein
said at the end of the Tractatus, our world is totally limited by our language.
It is what is beyond language that is interesting.