I think in proving an intelligent uncaused cause that is pure-actuality and completely simple, you can begin considering the question of why it would create.
Considering that such a being would lack any practical reason for creating anything because it is already everything that is necessary, one can conclude that there is something about it’s nature that is intrinsic to the reason why it creates things.
One can also infer from the fact of creation, that what God is essentially doing is sharing his existence with that which does not have to exist, and at the same time sustaining it in existence.
One can conclude from this that the only way of making intelligible sense of that act is by accepting the idea that God’s will and nature is Love and the act of creating a reality in which other personal beings emerge is a gift.
If 3 proves to be the only intelligible way of making sense of God’s creative act, one can begin to consider the intelligibility of God being love. If God is love and God doesn’t have to create, then it must be that God loves himself, but if God is one person then the act of loving only oneself would be a selfish act. One could try to resolve this by saying that God created to avoid being selfish. However this would be incorrect because God’s nature is neccesarily what it is and does not change and is not forced to change by any thing or possibility. Therefore it must be true that God’s nature is love even with out creation. But if God cannot be selfish, then one can argue that the only intelligible sense we can make of God’s nature is to say that God is already a community of persons and necessarily so because love by it’s very nature is an expression shared between persons.
Conclusion: God is love and also a community of persons in one nature. This doesn’t prove a trinity but it comes pretty darn close.
One could give the defeater that it is not clear what love is or what it would mean to be a nature that is love and what about the existence of evil. But i think if it’s the only intelligible way of making sense of God’s creative act, then the rest follows necessarily.
What do you think?