Background: Countries achieving control of COVID-19 after an initial outbreak will continue to face the risk of SARS-CoV-2 resurgence. This study explores surveillance strategies for COVID-19 containment based on polymerase chain reaction tests. Methods: Using a dynamic SEIR-type model to simulate the initial dynamics of a COVID-19 introduction, we investigate COVID-19 surveillance strategies among healthcare workers, hospital patients, and community members. We estimate surveillance sensitivity as the probability of COVID-19 detection using a hypergeometric sampling process. We identify test allocation strategies that maximise the probability of COVID-19 detection across different testing capacities. We use Beijing, China as a case study. Results: Surveillance subgroups are more sensitive in detecting COVID-19 transmission when they are defined by more COVID-19-specific symptoms. In this study, fever clinics have the highest surveillance sensitivity, followed by respiratory departments. With a daily testing rate of 0.07/1000 residents, via exclusively testing at fever clinic and respiratory departments, there would have been 598 [95% eCI: 35, 2154] and 1373 [95% eCI: 47, 5230] cases in the population by the time of first case detection, respectively. Outbreak detection can occur earlier by including non-syndromic subgroups, such as younger adults in the community, as more testing capacity becomes available. Conclusions: A multi-layer approach that considers both the surveillance sensitivity and administrative constraints can help identify the optimal allocation of testing resources and thus inform COVID-19 surveillance strategies.