Can Media Encoder transcode H.264 .MP4s with original timecode?

Is there a way for Media Encoder to create H.264 .MP4s that retain the original media's timecode?

Original timecode is retained when transcoding to for e.g. ProRes 422 Proxy, just not H.264 MP4.

It can be done in DaVinci Resolve; I'd love to know how to do it in Media Encoder.