Predicting which hypothetical inorganic crystals can be experimentally realized remains a central challenge in accelerating materials discovery. SyntheFormer is a positive-unlabeled framework that learns synthesizability directly from crystal structure, combining a Fourier-transformed crystal periodicity (FTCP) representation with hierarchical feature extraction, Random-Forest feature selection, and a compact deep MLP classifier. The model is trained on historical data from 2011 through 2018 and evaluated prospectively on future years from 2019 to 2025, where the positive class constitutes only 1.02 per cent of samples. Under this temporally separated evaluation, SyntheFormer achieves a test area under the ROC curve of 0.735 and, with dual-threshold calibration, attains high-recall screening with 97.6 per cent recall at 94.2 per cent coverage, which minimizes missed opportunities while preserving discriminative power. Crucially, the model recovers experimentally confirmed metastable compounds that lie far from the convex hull and simultaneously assigns low scores to many thermodynamically stable yet unsynthesized candidates, demonstrating that stability alone is insufficient to predict experimental attainability. By aligning structure-aware representation with uncertainty-aware decision rules, SyntheFormer provides a practical route to prioritize synthesis targets and focus laboratory effort on the most promising new inorganic materials.