Somatic copy number alterations (CNAs) are hallmarks of cancer. Current algorithms that call CNAs from whole-genome sequenced (WGS) data have not exploited deep learning methods owing to computational scaling limitations. Here, we present a novel deep-learning approach, araCNA, trained only on simulated data that can accurately predict CNAs in real WGS cancer genomes. araCNA uses novel transformer alternatives (e.g. Mamba) to handle genomic-scale sequence lengths (∼1M) and learn long-range interactions. Results are extremely accurate on simulated data, and this zero-shot approach is on par with existing methods when applied to 50 WGS samples from the Cancer Genome Atlas. Notably, our approach requires only a tumour sample and not a matched normal sample, has fewer markers of overfitting, and performs inference in only a few minutes. araCNA demonstrates how domain knowledge can be used to simulate training sets that harness the power of modern machine learning in biological applications.