My oldest was an only child for 7 years (my kids are spread wide apart age-wise) and he and his brother really weren't play buddies until he was probably 11, and at that point he was still more interested in kids his own age rather than his brother. Before his brothers were around, he was out and about playing and we had a houseful of neighborhood boys all the time.

Getting your child involved in activities is a bit different than arranging play dates. Yes, they are social interactions, but they are centered around activities rather than just general play, and it isn't something you have to "arrange" because it is routine. And you don't have to get agreement from other parents because it isn't about the parents choosing to meet up; it is about the kids and their activities.