Fog collection is a promising solution to the worldwide water scarcity problem and is also of vital importance to industrial processes, such as recapturing water in cooling towers and mist elimination. To date, numerous studies have investigated the fog collection rate, a parameter that denotes the average performance over a long period of time. However, the initial period (referred to as onset time) between the start of the fog-laden flow and the actual collection of the captured liquid (a delay in time caused by droplet growth to a critical weight that exceeds droplet-surface retention force) has not been systematically understood. A longer onset time may result in a more serious clogging issue that deteriorates the collection rate and, hence, understanding this phenomenon is important. Here, we study how the onset time is determined by the capture and transport of fog using individual, vertical wires with various surface wettabilities and diameters, under different wind speeds. This approach allows us to derive a scaling law that correlates the onset time with the fog capture process and droplet-surface retention force, governed by aerodynamics and interfacial phenomena, respectively. In particular, the onset time decreases with an increasing rate of fog capture or a decreasing droplet-surface retention force. This study introduces an important aspect in the evaluation of fog collection and provides insights for the optimal design of fog collectors and mist eliminators.