There are many things to consider. What type of system is our existence (the universes system)? Is it: everything that exists; is it open, is it closed; is it mostly closed but part open; is it directed by another system, or is it self-organising?
Let's state outright a hypothesis that our system (the universe) and nature is as follows: a) mostly informationally closed, with perhaps some sensory capacity of a system external to it b) self-organising (in that nature is clearly mostly a heterogeneous non-linear system except for the subatomic world where homogeneous systems can be studied.
These points infer a universe that has fractal self-similarity. In other words, if human consciousness is a self-organising system with various nearly closed states ---information-, organisation-, operational- closure etc---then this maybe the trait of the whole system ie, the universe.
In such systems, you get two forms of causation: upward causation (one thing leads to another: cause to effect) and downward causation (the emergent system's outputs impact the systems beneath it.
Thus, you get self-reference due to downwards causation.
We can call upwards causation 'bottom up', and downwards causation 'top down'. If you think of human perception, world views, philosophies etc, most systems derived from these set rules and principles which are then imposed upon the people. This would be downwards causation, as the emergent phenomena of consciousness impacts upon the behaviour of our sub-atomic underpinnings.
Yet, also there is external impact upon our society that can alter top-down system control: disasters, war, viral outbreaks, etc. Covid response is an example of where our societies adapted their own responses to a dangerous viral outbreak. The virus didn't tell our society how to react; rather, the internal structures of our governments put into action emergency measures that arose from our own systems.
All of that arose from the subatomic beginnings of our universe if current ideas on big bang universe beginnings are correct.
So then we have to reconcile a simple system of beginnings that via bottom up interactions somehow became emergent amd self-organising to the point where internal modelling of our environment enabled us to respond in a coordinative fashion to survive dangerous viral outbreaks (or wars etc).
The purpose (or any purpose) only has meaning relevant to our internal models; whereas, studying the processes that are underlying reality lead us to another direction---self-understanding.
So why we exist arises from content; whereas, how we exist comes about from the study of simple and then complex systems.