Effective earthquake risk reduction relies on accurate site-specific evaluations, which require models capable of representing the influence of local site conditions on ground motion characteristics. We address strong ground motion generation from time-domain accelerometer records and introduce the TimesNet-Gen, a deep generative framework. In this framework, site-specific generation is directly achieved through a station-restricted, Dirichlet-based latent space resampling strategy, without relying on explicit conditioning inputs or dimensionality reduction. Pre-trained on the AFAD dataset via self-supervised learning, the frozen model demonstrates robust cross-regional generalization by successfully generating station-specific NGA-West2 records without any fine-tuning. Model performance is evaluated by comparing the distributions of generated and real records in the log-HVSR space, alongside the joint analysis of peak ground acceleration and fundamental site frequency. As a baseline, we construct a spectrogram-based conditional variational autoencoder (CVAE) explicitly formulated for station-specific latent space modeling. The results show strong station-wise alignment, consistent cross-regional ground motion synthesis, and a favorable comparison with a spectrogram-based conditional variational autoencoder baseline, demonstrating that the model empirically maintains the essential physical coupling between frequency content and peak amplitude. Our codes are available via https://github.com/brsylmz23/TimesNet-Gen.