First-shot (FS) unsupervised anomalous sound detection (ASD) is a brand-new task introduced in DCASE 2023 Challenge Task 2, where the anomalous sounds for the target machine types are unseen in training. Existing methods often rely on the availability of normal and abnormal sound data from the target machines. However, due to the lack of anomalous sound data for the target machine types, it becomes challenging when adapting the existing ASD methods to the first-shot task. In this paper, we propose a new framework for the first-shot unsupervised ASD, where metadata-assisted audio generation is used to estimate unknown anomalies, by utilising the available machine information (i.e., metadata and sound data) to fine-tune a text-to-audio generation model for generating the anomalous sounds that contain unique acoustic characteristics accounting for each different machine type. We then use the method of Time-Weighted Frequency domain audio Representation with Gaussian Mixture Model (TWFR-GMM) as the backbone to achieve the first-shot unsupervised ASD. Our proposed FS-TWFR-GMM method achieves competitive performance amongst top systems in DCASE 2023 Challenge Task 2, while requiring only 1% model parameters for detection, as validated in our experiments.