The question of why Perumal exists and why this universe was created does not arise at all as this query will be relevant only when something is created new; Perumal exists eternally and so is this universe.
Before creation began and during the time of universal dissolution (pralaya kalam), the universe and other beings were in subtle forms. To enjoy the experience of playing with His children, Perumal beings the creation – this is similar to a mother waking up a child that has been sleeping for a long time to feed that child.
Instead of suffering in this material world, if we reach Srivaikuntham, where there no hunger and thirst, and we can have supreme and eternal happiness. We can be with Perumal like how children live with parents. Perumal incarnates to make us realize this and leads us to Him.
Like how parents care for their children, Perumal does all of these because of his affection for us, His children.