Spatio-temporal point processes (STPPs) are potent mathematical tools for modeling and predicting events with both temporal and spatial features. Despite their versatility, most existing methods for learning STPPs either assume a restricted form of the spatio-temporal distribution, or suffer from inaccurate approximations of the intractable integral in the likelihood training objective. These issues typically arise from the normalization term of the probability density function. Moreover, existing works only provide point prediction for events without quantifying their uncertainty, such as confidence intervals for the event's arrival time and confidence regions for the event's location, which is crucial given the considerable randomness of the data. To tackle these challenges, we introduce SMASH: a Score MAtching-based pSeudolikeliHood estimator for learning marked STPPs. Specifically, our framework adopts a normalization-free objective by estimating the pseudolikelihood of marked STPPs through score-matching and predicts confidence intervals/regions for event time and location by generating samples through a score-based sampling algorithm. The superior performance of our proposed framework is demonstrated through extensive experiments on both point and confidence interval/region prediction of events.