To address the challenges of identifying and warning gas turbine engine instability under dynamic conditions—particularly in the presence of strong noise and low signal-to-noise ratios—this paper proposes a identification and warning method based on Adaptive Wavelet Synchrosqueezed Transform (AWSST) and dynamic threshold calibration. The method continuously collects static pressure signals at the compressor outlet via a sliding window, then applies low-pass filtering and downsampling to suppress noise. AWSST combines dynamic scale discretization with synchronous compression to extract instantaneous time–frequency features, enhancing the detection of weak instability patterns. A k-parameter-based adaptive thresholding mechanism is further introduced to adjust sensitivity in real time by analyzing current energy distributions and historical operation data. This enables dynamic calibration of thresholds, ensuring both timely response and robustness across varying conditions. Simulation results demonstrate that the proposed method effectively identifies early signs of instability in real time and issues reliable warnings, even under noisy environments, while maintaining low computational cost. These findings confirm the method’s potential for engineering applications in onboard engine health monitoring and early fault prevention.