Share with 'Start at' tag in YouTube iOS app How can I share video with &quot;Start at&quot; option in YouTube iOS app?
copy the link and append ?=tXs to it, with X being the number of seconds into the video you want to share at. It's also possible to specify minutes, using ?=tXmYs, where X is minutes and Y is seconds.
I don't think there's an easy way of selecting the time, you have to work it out manually.