It depends on how you look at it.
If we can assume God created us, along with the universe, time, matter, etc., it is safe to assume that he did it for himself (there not being anyone else to create us for.) We exist for no other reason than for God's pleasure. God created the physical laws by which everything in the known universe abides, and also the rules that govern the way we act and feel. These "Internal rules" differ greatly between male and female, and somewhat more limitedly inside genders. But, he also knows the end of all things, and he knows all of the rules inside our heads. He knows what choice we will make every time. So, why would the almighty ever have an interest in us?
I believe the answer, in part lies in the fact that God exists outside of time. How else could it be that God has always existed, always will exist, and exists today, without ever changing? How could God have created time if he were trapped in it? God sees the whole picture at once. He can interfere in a specific time, but I believe that the way he perceives it is fundamentally different.
God is interested in a personal relationship with us. But, he also created our free will that can cause us to reject him. Although he knows who will and will not accept him in the end, he is intimately interested in revealing himself to each of us. It's not the ending he's worried about, it's the relationship. God has created the angels, but I believe that we are able to connect with God in ways that the angels cannot dream of. Sure, I guess God could be doing bigger things with his time, but his character compels him to love and seek him out. Can anyone truly understand and explain God?
(In response to the logical question)
Just as God exists outside of time, so he exists outside of the universe. After all, how could his existence be dependent upon something he created? Therefore, if the essence of God is something from outside the universe, time and all physical laws we know, which were created by him, I think the question is rendered fairly pointless. God exists outside of all quantitative properties we know, so I'd say it's fairly reasonable to say that he doesn't necessarily have a beginning.