Can a grandparent or third party seek visitation with a child whose parents were married at the time the child was born but are now divorced?

Only in limited circumstances. Once three months have passed since the divorce, the child’s grandparents have this option at any time. As for everyone else, a strict reading of A.R.S. § 25-409(C) would suggest that persons other than grandparents have a limited one-time opportunity to file for visitation—and that is at the time the parents are getting divorced, and even, only if the person qualifies as in loco parentis, meaning they have a parent-like relationship with the child. This again would be a strict reading of the statute; it is possible courts may not read it as strictly.