Radar-based microwave imaging has been proposed as a complementary modality for early-stage breast cancer screening. This paper presents an algorithm that may be used to accurately predict the time-of-arrival (TOA) of a tumor response contained in sample data acquired from a small number of antennas in a realistic scenario. The TOA information may be used by many of the existing radar-based methods to detect and localize a tumor response. The robustness of the algorithm is demonstrated with data generated from realistic numerical breast models.