Is it possible to set a starting time for a video in ffmpeg without encoding?

If you cut a video with ffmpeg without re-encoding, it will start at the last keyframe before the cut (or the next one after the cut depending on how you did it)

If you encode when you cut, the video will start at the correct time, but the keyframe will still be right where it was, the only thing that changed is that the file has lost some quality from the encode and the file now starts at exactly the frame where you cut it from; the frames before it are still there but just won’t be played.

I was wondering if there was a way to achieve this effect without actually encoding.

I figured using -itsoffset to set the pts_time would help but it seems to have no effect

ffmpeg -itsoffset 2.4 -i cut.mkv -c copy output.mkv

This does change the pts_time of output.mkv to 2.4, but the video still starts at timestamp 0. How would I make it start at 2.4 seconds instead?

I’ve found a couple similar questions but no good answer.