Do any denominations teach that humans exist before birth? I'm agnostic, and there is is a specific symmetry in the timeline of life, when looking at it over all time.

To me, a person does not exist before it is born, and does not exist after it died. During the lifetime, there is a period of growth, and a period of decay.

Looking at it from the beginning of time to the end of time, this has a symmetry that has a certain beauty in it, I almost feel the symmetry is spiritual.

Whether time is finite or not does not matter for it.

It would be interesting whether it is seen that a person exists between conception and birth, but does not fundamentally change the question.

Is there a concept comparable to this in any Christian denomination?

The important and beautiful aspect is the symmetry in spacetime.
I'm not sure if you'd include Mormonism as a Christian denomination, but the Mormon church definitely believes this. They believe that people were "Heavenly Father's" spirit children in heaven, who are now in the flesh on earth: Spirit Children of Heavenly Parents.