With the imminent relaxation of socio-economic restrictions, it becomes vital to assess its effect on the prevalence of acute infections within the population, as rapidly as possible. Currently available monitoring instruments for the COVID-19 pandemic have an inherent time delay of about 14 days, as they rely on confirmed infections, hospitalizations, and death numbers. These methods give Reff(t) (the number of infections caused by a single infected person), but their delay is a significant disadvantage when restrictions are released. If after relaxation, Reff(t) rises above 1, one will not be able to react adequately before two weeks have passed during which time the prevalence could significantly rise. Here, we propose the use of random testing to shorten this reaction time, by obtaining direct and modeling dependent information on Reff(t). Through random testing of between 2500 and 20000 people per day, we find that over periods significantly shorter than two weeks, it becomes possible to detect a dangerous increase in Reff with reasonable confidence.