Just stay active on it, do your part by answering queries.  A good platform with substance will always survive. People dint promote Quora, its content did its marketing. As long as the content stays relevant to someone's search the traffic is bound to come. 

Have patience and let it grow. Word of mouth is the best publicity any platform can get. I don't think I ever saw an Advertisement  for Google Search Engine on Television but still it is the best. 

However Celebrity interviews, Q& A sessions could prove to be a big publicity stunt for Musing. That would be a good marketing ploy. But still after that you need to have substance.