Upconversion (UC) in a molecular system is a process in which excitons produced by a multiple absorption of low-energy photons at long wavelengths undergo fusion to produce high energy excitons that consequently recombine to emit anti-Stokes shifted photons. Molecular systems for UC typically require a sensitizer. However, recent experiments show that UC in rubrene occurs even without the presence of the sensitizer. In this system, intermediate states are assumed to absorb photons at near-infrared wavelengths, which either absorb additional photons to populate the emissive singlet state or undergo fusion to generate triplets. The triplets can again undergo fusion to populate the excited singlet state. The final emission is around 600 nm. These models have been tested against the intensity dependence of the UC emission. Here, we have measured the kinetics of UC in rubrene by using intensity modulated photoexcitation at 800 nm to better understand the underlying mechanism. The models of UC that have been proposed so far do not agree with our measurements. Our results show that the yield of UC lags behind excitation significantly, indicating that triplet states are directly excited from the ground state, and their fusion, which depends on the population, becomes prominent after a certain build up time. While the intermediate states could form dynamically after the UC has been initiated and enhance the process, further sensitive absorption measurements are necessary to understand the role of the intermediate states in the process. Our results are important in finding new routes to enhance UC in pristine organic semiconductors for applications in photovoltaics, lasers, bioimaging, optical devices, and lighting.