To predict the boundary-layer transition location over a flat plate across varying Mach numbers, an efficient method was developed for small-sample settings. Flow-field disturbance datasets across multiple Mach numbers were generated using the nonlinear parabolized stability equations, with Ma=0.01 designated as the source domain and Ma=0.1, 0.2, 0.4, 0.8, 1.6 as target domains. The influence of Mach number variations on transition patterns was systematically analyzed. A convolutional neural network model was employed to map flow field patterns to transition locations, incorporating a transfer learning strategy with progressive unfreezing and layer-wise learning rates. Results demonstrate that transfer learning significantly outperforms direct training: for Ma≤0.4, only 1/10 of the target domain samples are required to achieve a mean absolute error below 2.04% of the average ground-truth value; for Ma≥0.8, a progressive domain adaptation strategy controls the error within 6.19%. The approach enhances transition prediction under small-sample conditions and provides a reliable technical pathway for cross-condition flow modeling.