3GPP Release~16 specifies how a 5G system can operate as a transparent IEEE~802.1 TSN bridge, yet no existing simulation framework implements the complete bridge architecture with end-to-end QoS mapping through the SDAP layer, per-flow Data Radio Bearer selection, and IEEE~802.1AS transparent clock behaviour with measured residence time. Existing tools model either QoS mapping without time synchronisation, or time synchronisation without a data plane. This paper presents nascTime, a simulation framework built on OMNeT++~6.3, INET~4.6, and Simu5G that implements the full 3GPP 5G-TSN bridge model. The NW-TT and DS-TT are realised as modular compound modules that integrate with INET's \texttt{LayeredEthernetInterface} and streaming PHY. QoS mapping traverses the complete PCP\,$\rightarrow$\,DSCP\,$\rightarrow$\,QFI\,$\rightarrow$\,SDAP/DRB pipeline, and gPTP frames are transported through the simulated 5G radio path via L2-in-GTP-U encapsulation with per-message residence-time correction. We validate the framework with a three-endpoint factory topology under both ideal and fading channel conditions. In the ideal scenario, high-priority traffic achieves 99.9\% delivery with a mean end-to-end delay of 2.58\,ms, while the measured 5GS residence time exhibits a variance below 0.2\,$μ$s. Under a fading channel, residence-time variance increases to 48\,$μ$s, confirming that the framework captures radio-induced timing effects absent from abstract-delay simulators. nascTime is publicly available and constitutes the first full-stack 5G-TSN bridge simulation with SDAP-based QoS differentiation and measured IEEE~802.1AS transparent clock behaviour.

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