It’s incredible why something as simple as this was not documented anywhere.
Anyway, if you were looking to use the YouTube embed shortcode on WordPress and wanted to start the clip at a certain time, this is what you use:
Append this to the end of your YouTube URL so that the URL looks like this:
I removed the square parentheses at the start and end to avoid the video embed. 150 refers to 150 seconds (i.e. 2min30s), so do the necessary conversion for your preferred start time.
Hope this helps someone out there.