Traditionally, the guy should initiate the first kiss, but in reality, either person can.
According to etiquette books, the male in a relationship should initiate the first kiss. However, societal norms are evolving, and either partner can initiate this intimate gesture. In many modern relationships, the first kiss occurs with the man initiating, but there are no hard and fast rules dictating this. Kisses on the first date are often perfunctory, mechanical, or purely out of obligation.