Ask about a million dollar question, this is one of them. I wish I knew the answer for sure.
I believe we exist even before we realize that we exist. The realization or perceiving of our existence happens to us because of consciousness. We get the ability to think, choose, decide after we have consciousness. The consciousness itself happens to us, we did not decide or choose it. We do not choose in which body, family, city, or country we want the consciousness to manifest upon us. We are able to create an identity for us, differentiate among things, and create a history of ourselves in our brain only after consciousness manifests upon us, the perceiving one.
So, trying to figure out why do we exist, is just like a computer software trying to figure out a procedure that the programmer has never coded in the answer for. At least with normal sensing mechanisms in us, I think we will not be able to figure it out. May be there is way to know the answer by activating the sixth sense or third eye or whatever the extra power is called; through science, meditation, self-inquiry, enlightenment...etc. I for sure do not have any of them, except my full attention to this present moment.
My logic is that, if we existed even before were able to realize that we exist, we will exist even after we are no longer able to perceive our existence. Therefore, we were always there and will always be. The question of why comes only when thoughts dance on brain and only during the perceiving phase. Anything that is only relevant on one phase cannot be a TRUE thing. Thus, asking the question why we exist is like computer program trying to figure out a procedure that is not defined in the program. The outcome will be that the computer will freeze and there will be no resolution. Alas, the poor computer will never be able to figure out the reality beyond the program because it does not have any extra ability to perceive any other dimension. So is the case with us trying to figure out why we exist.
In grand scheme of things, I believe, this question, although not trivial, is not relevant. However, it will help us get near our own TRUTH, which if we all derive carefully, must be the same.