Tandem Mass Spectrometry is a cornerstone technique for identifying unknown small molecules in fields such as metabolomics, natural product discovery and environmental analysis. However, certain aspects, such as the probabilistic fragmentation process and size of the chemical space, make structure elucidation from such spectra highly challenging, particularly when there is a shift between the deployment and training conditions. Current methods rely on database matching of previously observed spectra of known molecules and multi-step pipelines that require intermediate fingerprint prediction or expensive fragment annotations. We introduce a novel end-to-end framework based on a transformer model that directly generates molecular structures from an input tandem mass spectrum and its corresponding molecular formula, thereby eliminating the need for manual annotations and intermediate steps, while leveraging transfer learning from simulated data. To further address the challenge of out-of-distribution spectra, we introduce a test-time tuning strategy that dynamically adapts the pre-trained model to novel experimental data. Our approach achieves a Top-1 accuracy of 3.16% on the MassSpecGym benchmark and 12.88% on the NPLIB1 datasets, considerably outperforming conventional fine-tuning. Baseline approaches are also surpassed by 27% and 67% respectively. Even when the exact reference structure is not recovered, the generated candidates are chemically informative, exhibiting high structural plausibility as reflected by strong Tanimoto similarity to the ground truth. Notably, we observe a relative improvement in average Tanimoto similarity of 83% on NPLIB1 and 64% on MassSpecGym compared to state-of-the-art methods. Our framework combines simplicity with adaptability, generating accurate molecular candidates that offer valuable guidance for expert interpretation of unseen spectra.