Historical records show that culture can increase exponentially in time, e.g., in number of poems, musical works, scientific discoveries. We model how human capacities for creativity and cultural transmission may make such an increase possible, suggesting that: (1) creativity played a major role at the origin of human culture and for its accumulation throughout history, because cultural transmission cannot, on its own, generate exponentially increasing amounts of culture; (2) exponential increase in amount of culture can only occur if creativity is positively influenced by culture. The evolution of cultural transmission is often considered the main genetic bottleneck for the origin of culture, because natural selection cannot favor cultural transmission without any culture to transmit. Our models suggest that an increase in individual creativity may have been the first step toward human culture, because in a population of creative individuals there may be enough non-genetic information to favor the evolution of cultural transmission.