Happy first birthday wishes include statements like, "Wow, I can't believe you've already turned one. You're so beautiful/handsome. Happy 1st birthday!" Statements that the parents of the one-year-old will enjoy are best because they're the ones who will be reading the message.
Wishing the one-year-old future years that are just as enjoyable and blissful as their first also makes a great birthday wish. If the little one is the first grandchild or child in the family, loved ones can make sure they are the first one to wish the first baby a happy first birthday. Birthday wishes can even state that this will only be the first of many happy birthdays for the child.