TCP slow-start grows the congestion window exponentially, aims to quickly probe the throughput of the network path. Stopping this growth at the wrong time can affect the overall network performance. In this paper, we introduce StopEG, an efficient mechanism to accurately and quickly detect when to stop this exponential growth. StopEG reacts to the changes on congestion window size rather than traditional congestion signals such as packet loss. We show that theoretically the number of inflight packets in the forward path is no more than 56.8% of all the inflight packets when the bottleneck link is unsaturated, and use this value as the threshold to stop the exponential growth. StopEG is evaluated through simulations in ns-3 by incorporating it into Google's BBR congestion control algorithm. Simulation results demonstrate its effectiveness in BBR, with a reduction of ≈68% in the length of the bottleneck queue when new connections are initiated.