The Massive Access Problem of the Internet of Things (IoT) occurs at the uplink Medium Access Control (MAC) layer when a massive number of IoT devices seek to transfer their data to an IoT gateway. Although recently proposed predictive access solutions that schedule the uplink traffic based on forecasts of IoT device traffic achieve high network performance, these solutions depend heavily on the performance of forecasters. Hence, the design and selection of forecasting schemes are key to enabling massive access for such predictive access solutions. To this end, in this paper, first, we develop a framework that emulates the relationship between the IoT device class composition in the coverage area of an IoT gateway and the resulting network performance by virtue of an Artificial Neural Network (ANN). Second, based on this framework, we develop the Dynamic Automatic Forecaster Selection (DAFS) method, which selects the best-performing forecasting scheme for predictive access, in particular for  Joint Forecasting-Scheduling (JFS), in a manner that adapts dynamically to a changing number of IoT devices in each device class in the coverage area. We evaluate the performance of DAFS via simulations and show that our method is able to achieve at least $80\%$ of the best performance that can be attained for both throughput and energy consumption. Furthermore, we demonstrate that DAFS is robust with respect to the selection of architectural parameters and has a reasonable computation time for real-time IoT applications. These results imply that DAFS holds the potential for practical implementation at IoT gateways in order to enable massive access under a dynamically changing composition of IoT devices.