We document quasi-experimental evidence against the common assumption in the matching literature that agents have full information on their own preferences. In Germany’s university admissions, the first stages of the Gale-Shapley algorithm are implemented in real time, allowing for multiple offers per student. We demonstrate that nonexploding early offers are accepted more often than later offers, despite not being more desirable. These results, together with survey evidence and a theoretical model, are consistent with students’ costly discovery of preferences. A novel dynamic multioffer mechanism that batches early offers improves matching efficiency by informing students of offer availability before preference discovery.