Motivated by the challenges in last-mile delivery operations, we consider a natural dynamic staffing problem in which a decision-maker sequentially hires staff over a finite time horizon to meet an unknown target demand at the end. The decision-maker also receives a sequence of predictions about the demand that become increasingly more accurate over time. Consequently, the decision-maker prefers to delay hiring decisions to avoid overstaffing. However, workers' availability decreases over time, resulting in a fundamental trade-off between securing staff early (thus risking overstaffing) versus hiring later based on more accurate predictions (but risking understaffing).