Crowdsourced delivery platforms face the unique challenge of meeting dynamic customer demand using couriers not employed by the platform. As a result, the delivery capacity of the platform is uncertain. To reduce the uncertainty, the platform can offer a reward to couriers that agree to be available to make deliveries for a specified period of time, i.e., to become scheduled couriers. We consider a scheduling problem that arises in such an environment, i.e., in which a mix of scheduled and ad-hoc couriers serves dynamically arriving pickup and delivery orders. The platform seeks a set of shifts for scheduled couriers so as to minimize total courier payments and penalty costs for expired orders. We present a prescriptive machine learning method that combines simulation optimization for offline training and a neural network for online solution prescription. In computational experiments using real-world data provided by a crowdsourced delivery platform, our prescriptive machine learning method achieves solution quality that is within 0.2%-1.9% of a bespoke sample average approximation method, while being several orders of magnitude faster in terms of online solution generation.