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Effective earthquake risk reduction relies on accurate site-specific evaluations. This requires models that can represent the influence of local site conditions on ground motion characteristics. In this context, data driven approaches that learn site controlled signatures from recorded ground motions offer a promising direction. We address strong ground motion generation from time-domain accelerometer records and introduce the TimesNet-Gen, a time-domain conditional generator. The approach uses a station specific latent bottleneck. We evaluate generation by comparing HVSR curves and fundamental site-frequency $f_0$ distributions between real and generated records per station, and summarize station specificity with a score based on the $f_0$ distribution confusion matrices. TimesNet-Gen achieves strong station-wise alignment and compares favorably with a spectrogram-based conditional VAE baseline for site-specific strong motion synthesis. Our codes are available via this https URL.