That ended up being on a slower timeframe than I think we had imagined. Yes, we shared some classic children's literature when they were young, but it took a while for CG to develop an interest in the television, music, and film that consumes her parents' lives. AA, meanwhile, has always gone his own way and developed his own obsessions; we worried, early on, that he would have nothing to talk about with his peers, but it turns out that Pokemon is a universal language (thankfully).
Another factor, though, is that it turns out the easiest way into popular culture's archival depths (aka the stuff that was meaningful to us when we were younger) is by way of current culture. And those entry points need to have some family appeal. They need to be things that we can watch or listen to with our child. CBS's Supergirl, for example; we made plans early on to include CG in our viewing of it, based on the creative people involved, its empowering messages, and the geek appeal factor. But once we're all hooked, when the show makes references to other parts of the DC universe (or even does a version of a classic story, like its retelling of Alan Moore's "For the Man Who Has Everything"), it's a simple matter to give those ancillary materials to CG and let her expand the connections.
We all treasure the moments when we bond with our children over shared culture. But those moments aren't really the heart and soul of a cultural education. As suggested by those records of Noel's dad and those books of my parents, the most important thing is to leave a lot of culture lying around, and wait for your kids to burrow their way in, by any route they choose. CG uses our Amazon Echo to stream music from our collection while she reads, and sometimes we can suggest other artists she might like. She developed her love of comic strips from the many collections with which we seeded her shelf. But as rich as our libraries might be, they'd be a prison if that's all she ever explored. She made her own way to manga and anime, and together she and Archer have ventured into gaming and design, areas their parents would never have been able to lead them.
And now they teach us, and amaze us. That's the part that we didn't know enough, years ago, to anticipate, and it's the part that now seems most miraculous.