Sparse mobile crowdsensing (MCS) is an emerging paradigm that collects data from a subset of sensing areas and then infers data from other areas. However, there is a shortage or uneven distribution of workers when sparse MCS is applied. Therefore, with a limited budget, it is important to prioritize the involvement of the more important workers in data collection. Additionally, many sparse MCS applications require timely data. Consequently, this study considers data freshness, with age of information (AoI) serving as a freshness metric. To address these challenges, a simplified AoI-aware sensing and inference (SASI) framework is proposed in this study. This framework aims to optimize AoI and inference accuracy by selecting suitable workers for data collection under budget constraints and accurately capturing spatiotemporal relationships in sensed data for inference. Moreover, limited budgets and worker availability may result in a reduced volume of data. Thus, methods for streamlining data inference models are also proposed to enhance inference efficiency. Experiments have substantiated the superiority of this framework in practice.