Understanding the ultrafast transport properties of charge carriers in transition metal dichalcogenides is essential for advancing technologies based on these materials. Here, we study MoSe2 crystals with thicknesses down to the monolayer, combining ultrafast spatiotemporal microscopy and quantitative microscopic modelling. Crucially, we obtain the intrinsic ultrafast transport dynamics by studying suspended crystals that do not suffer from detrimental substrate effects. In mono- and bilayer crystals, we identify four sequential transport regimes. The first two regimes involve high-energy non-thermalized and quasi-thermalized carriers that propagate rapidly with diffusivities up to 1000 cm2/s. After ~1.5 ps, a remarkable third regime occurs with apparent negative diffusion, finally followed by exciton propagation limited by trapping into defect states. Interestingly, for trilayer and thicker crystals, only the first and last regimes occur. This work underscores the role of traps and dielectric environment in electron transport, offering valuable insights for the development of (flexible) (opto)electronic applications.