We present a computationally efficient methodology for screening microporous materials for adsorption-based gas separation. Specifically, we develop and employ artificial neural network (ANN)-based surrogate models that increase the speed of approximating transient adsorption behavior and breakthrough times by several orders of magnitude without compromising the predictive capability of a high-fidelity process model. We introduce the concept of breakthrough event times and develop ANN-based surrogate models for their accurate prediction. Our results for numerous hypothetical adsorbents indicate that the effects of different materials-centric metrics are well-captured by the column breakthrough times at the process scale, thus providing a scale-bridging measure toward a multiscale framework for materials screening with process insights. Using the framework, we also screen the list of existing pure-silica zeolite frameworks for postcombustion carbon capture and natural gas purification applications. For postcombustion carbon capture, the top materials include WEI, JBW, and GIS, and for natural gas purification, the top materials are GIS, SIV, and DFT. For any binary gas mixture, the developed ANN models can be leveraged for (i) fundamentally studying the materials properties that determine the dynamic breakthrough times and gas concentration profiles and (ii) high-throughput adsorbent screening and identification of novel materials with desired properties.