When a lytic bacteriophage infects a cell, it hijacks the cell's resources to replicate itself, ultimately causing cell lysis and the release of new virions. As phages function as obligate parasites, each stage of the infection process depends on the physiological parameters of the host cell. Given the inherent variability of bacterial physiology, we ask how the phage infection dynamic reflects such heterogeneity. Here, we introduce a pioneering assay for investigating the kinetics of individual infection steps by a single T7 phage on a single bacterium. The high-throughput, time-resolved nature of the assay allows us to monitor the infection progression simultaneously in multiple cells, revealing substantial heterogeneity in each step and correlations between the infection dynamics and the infected cell's properties. Simulations of competing phage populations with distinct lysis time distributions indicate that this heterogeneity can have considerable impact on phage fitness, recognizing variability in infection kinetics as a potential evolutionary driver of phage-bacteria interactions.