Why Did God Create Us?
God is absolutely simple, unchanging, and continuously creating and sustaining all existence (including space and time, therefore he is beyond them). The nature or essence of God is Goodness. He donates being and out of nothingness, being simply is. This brings about the spiritual and material worlds with their hierarchy (which God himself transcends). What are the Universal Intellect and Universal Soul?
As far as why our souls comes here (are born) into this physical world, it is because this is the place where our souls have the ability to elevate, through dealing with trials and suffering. In the higher spiritual worlds there is peace. Eternal souls do not suffer hardships there. When asked why there is suffering in this world, the Imams have responded saying if there was no suffering in this world then there would be no difference between this world and paradise.
The lower material world gets generated and its nature is such that it is temporal and changing due to interplay of space, time, matter, etc. This allows for degeneration of whatever is material. Here souls can come to grow through how they deal with difficulties, various situations, free will to perform good and bad deeds, etc. In this world there is suffering so it is an opportunity to do good by easing suffering of others. This allows us to partake in the above-mentioned Goodness. This opportunity is not present in the higher spiritual worlds.