There are some kids club activities that involve characters - and even some with Goofy. It's worth asking the kid's club staff what activities involving Goofy are on the schedule so you can look for them in the navigators on your cruise and make sure your child doesn't miss them.
We've often encountered Goofy wandering around on deck, but he also does scheduled meet-and-greets. You can always attend one, and have a nice conversation with Goofy's attendant about the situation. It might make a difference, but it might not - either way, the entertainment staff is fun to chat with!
To give you some examples of some of the amazing interactions we've had with characters on our cruises (and some of the reasons we keep returning to
DCL):
We took a transatlantic when my DD was 9, and by the second or third day, Minnie Mouse knew our daughter by name. It was the most adorable thing. Whenever we saw Minnie, she'd spell our DD's name out on someone's hand, be so excited to see her, and give her big hugs. It's one of the best memories we've had from a DCL cruise, and really made the cruise magical.
The characters have great memories, too. When my DD was 4 on a 4n Wonder cruise, we met Peter Pan and Wendy one evening. We were chatting and somehow in the course of the conversation, my DH commented that he's not a fan of the movie Alice in Wonderland because it's weird. The last day of the cruise they had a large-scale character signing with a bunch of characters sitting at a table in the atruim (they don't do this anymore). We encountered Peter first, who was sitting next to Wendy, who was sitting next to Alice. Peter leaned over to talk to Alice and tell her, "This guy thinks you're weird." It was one of the most awkward and memorable experiences! Peter in general is great - he's also invaded some of our meet group activities and hung out with us in the Promenade Lounge.