Repurposed drugs that are immediately available and safe to use constitute a first line of defense against new viral infections. Despite limited antiviral activity against SARS-CoV-2, several drugs are being tested as medication or as prophylaxis to prevent infection. Using a stochastic model of early phase infection, we find that a critical efficacy above 87% is needed to block viral establishment. This can be improved by combination therapy. Below the critical efficacy, establishment of infection can sometimes be prevented, most effectively with drugs blocking viral entry into cells or enhancing viral clearance. Even when a viral infection cannot be prevented, antivirals delay the time to detectable viral loads. This delay flattens the within-host viral dynamic curve, possibly reducing transmission and symptom severity. Thus, antiviral prophylaxis, even with reduced efficacy, could be efficiently used to prevent or alleviate infection in people at high risk.