Timely detection of an incoming epidemic wave remains essential for public health decision-making, especially within the renewed rise of COVID-19 cases in Europe linked to emerging late-2025 variants. However, statistical indicators based on short-term regression fitting face a fundamental trade-off: smaller temporal windows react quickly but generate false alarms, whereas longer windows are more stable but respond too late. This study formalizes and quantifies this responsiveness–stability trade-off using daily COVID-19 case data from the Our World in Data (OWID) repository for five European countries – Czechia, Germany, Poland, France, and Italy – spanning 2020–2025. A rolling linear regression model was applied to smoothed incidence curves, and an alarm was raised when the estimated slope became significantly positive (one-sided t-test, α = 0.05). Ground-truth wave onsets were defined as sustained growth in a 21-day moving-average trend lasting at least ten days. For each regression window w, two complementary metrics were evaluated: the false positive rate (FPR), describing spurious alarms, and the mean detection delay (MDD), quantifying the lag in identifying true wave onset. Short windows reduce delay but raise FPR, while long windows have the opposite effect. Normalizing the measures, particularly MDD to nMDD, and combining them both into a composite score S(w) = FPR(w) + nMDD(w) revealed a clear U-shaped dependence on w, with optimal values around 10–14 days. The approach offers a transparent, data-driven framework for evaluating early-warning sensitivity in epidemic surveillance systems.