I don't know if this counts as "conversion", and it happened back when TNG was still in reruns on TV, but it's still a fun story.
My nephew was about a year old at the time, just starting to develop a vocabulary. I build models as a hobby and with the exception of a couple of cars, everything I have is sci-fi. I was babysitting him one night. We were sitting in my room and TNG was on (don't remember what ep...doesn't matter anyway). At one point, I notice him looking back and forth from the TV to my model shelves. He recognized the model of the E-D as being the same one on TV. I showed him the model up close and told him "This is the Enterprise".
One year old and he's trying to say "Enterprise"!