Spatiotemporal data are being produced in continuously growing volumes by a variety of data sources and a variety of application fields rely on rapid analysis of such data. Existing systems such as PostGIS or MobilityDB usually build on relational database systems, thus, inheriting their scale-out characteristics. As a consequence, big spatiotemporal data scenarios still have limited support even though many query types can easily be parallelized. In this paper, we propose our vision of a native serverless data processing approach for spatiotemporal data: We break down queries into small subqueries which then leverage the near-instant scaling of Function-as-a-Service platforms to execute them in parallel. With this, we partially solve the scalability needs of big spatiotemporal data processing.