Here, we construct a waveguide-free WS2/graphene photodetector and apply the two-pulse coincidence (2PC) photoresponse technique via asynchronous optical sampling (ASOPS) to determine the hot carrier dynamics that contributes to the photocurrent. Upon 1560 nm excitation, the heterostructure photodetector exhibits two lifetime components with τfast  3 ps and τslow  500 ps. We attribute the τfast to a hot carrier injection and cooling, which we rationalize in terms of its super-linear power-dependence, the positive contribution to the photocurrent, and an increasing lifetime with decreasing temperature. We argue that the slow component resembles trapped holes in the TMDC, which is supported by its negative contribution to the photocurrent and its disappearance upon applying large biases. The fast hot carrier cooling and long circulation of electrons in the heterostructure affords a telecom C-band-suited photodetector with a simultaneously enhanced photoresponse speed and responsivity. Moreover, we show that the photodetection performance can be further increased by designing a vertical WS2/graphene/WSe2 device with an out-of-plane built-in electric field and the same hot carrier injection mechanism. For this device, the photocurrent on-off ratio is 3500 with an extrinsic response time of 1.71 ns and a responsivity of 0.18 A/W.