The COVID-19 pandemic has exerted a profound impact on the global economy and continues to exact a significant toll on human lives. The COVID-19 case growth rate stands as a key epidemiological parameter to estimate and monitor for effective detection and containment of the resurgence of outbreaks. A fundamental challenge in growth rate estimation and hence outbreak detection is balancing the accuracy-speed tradeoff, where accuracy typically degrades with shorter fitting windows. In this paper, we develop a machine learning (ML) algorithm, which we call Transfer Learning Generalized Random Forest (TLGRF), that balances this accuracy-speed tradeoff. Specifically, we estimate the instantaneous COVID-19 exponential growth rate for each U.S. county by using TLGRF that chooses an adaptive fitting window size based on relevant day-level and county-level features affecting the disease spread. Through transfer learning, TLGRF can accurately estimate case growth rates for counties with small sample sizes. Out-of-sample prediction analysis shows that TLGRF outperforms established growth rate estimation methods. Furthermore, we conducted a case study based on outbreak case data from the state of Colorado and showed that the timely detection of outbreaks could have been improved by up to 224% using TLGRF when compared to the decisions made by Colorado's Department of Health and Environment (CDPHE). To facilitate implementation, we have developed a publicly available outbreak detection tool for timely detection of COVID-19 outbreaks in each U.S. county, which received substantial attention from policymakers.