We discuss generic thermodynamic bounds on the moments of first-passage times of dissipative currents in nonequilibrium stationary states. These bounds hold generically for nonequilibrium stationary states in the limit where the threshold values of the current that define the first-passage time are large enough. The derived first-passage time bounds describe a tradeoff between dissipation, speed, reliability, and a margin of error and therefore represent a first-passage time analogue of thermodynamic uncertainty relations. For systems near equilibrium the bounds imply that mean first-passage times of dissipative currents are lower bounded by the Van't Hoff-Arrhenius law. In addition, we show that the first-passage time bounds are equalities if the current is the entropy production, a remarkable property that follows from the fact that the exponentiated negative entropy production is a martingale. Because of this salient property, the first-passage time bounds allow for the exact inference of the entropy production rate from the measurements of the trajectories of a stochastic process without knowing the affinities or thermodynamic forces of the process.