Hollow-core fibers offer superior loss and latency characteristics compared to solid-core alternatives, yet the geometric complexity of nested antiresonance nodeless fibers (NANFs) makes traditional optimization computationally prohibitive. We propose a high-efficiency, two-stage machine learning framework designed to identify high-performance NANF designs using minimal training data. The model employs a neural network (NN) classifier to filter for single-mode designs (suppression ratio $\ge$ 50 dB), followed by a regressor that predicts confinement loss (CL). By training on the common logarithm of the loss, the regressor overcomes the challenges of high dynamic range. Using a sparse data set of only 1,819 designs, all with CL greater or equal to 1 dB/km, the model successfully identified optimized designs with a confirmed CL of 0.25 dB/km. {This demonstrates the NN has captured underlying physical behavior and is able to extrapolate to regions of lower CL. We show that small data sets are sufficient for stable, high-accuracy performance prediction, enabling the exploration of design spaces as large as $14e6$ cases at a negligible computational cost compared to finite element methods.