INFLUENCE FROM FRIENDSMiroku and Sango didn't only find love by themselves, they were influenced a bit by their comrades through out the series. With an extra push, they were able to understand that they are right for each other.
Kagome, InuYasha, Shippou, and even Kirara all saw their relationship blossoming from the outskirts. Kagome often asked Sango about her feelings towards Miroku. Although Sango usually denied them, Kagome would just smile at her, knowing that that isn't true. However, Sango would also tease Kagome about InuYasha as well. They had a simple girlfriend relationship where they would talk about the boys in their lives. InuYasha and Shippou would often see Miroku flirt with other women, and instantly realize he is goofing up because Sango is right there as well. They were often scared for Miroku's well-being, knowing that he was about to be slapped by an angry Sango! The episode where everyone was drunk, and Sango was throwing herself at InuYasha, cracks me up because of InuYasha's face. He knows Miroku must be angry, so he tried to push Sango away from him. This shows that InuYasha is well aware of his friends feelings for Sango.
Although none of the characters outwardly pushed these two together, they acknowledged that a relationship was forming. They allowed Miroku and Sango to have alone time as well, which was an added bonus for them to really bond on a one-on-one basis. This also shows that none of them had any major concerns with Sango liking Miroku, or Miroku liking Sango. When your friends also support you being together, that is a great sign! That means that the people who know you the most can appreciate your love choice and realize that you two are a great match. And that they are!