FFMPEG save filename with livestream timestamp

I usually save clips from livestreams with FFMPEG, I do it like this:

ffmpeg -i livestreamURL.m3u8 -c copy -f segment -strftime 1 -segment_time 01:00:00 source_%H-%M-%S.mp4

But instead of using Hours, Minutes and Seconds from today’s time, I’d like the file to have the timestamp from the livestream, so if the stream has been running for one hour and twenty minutes I’d like the filename to include that, for example 1-20-00.mp4

So I’m wondering if it’s possible to do that with an FFMPEG command?