Downloading earlier segments from a live m3u8 playlist
You need to download the m3u8 itself, look at the entries and see if the individual TS filenames are entirely regular i.e. no signatures which vary with each entry, and the varying elements that are present can be deduced.

If so, then simply work backwards i.e. if the playlist you download has entries file_03532.ts, file_03533.ts, file_03534.ts..., then file_03529.ts, file_03530.ts, file_03531.ts.. would be the earlier entries. You can then use a download manager that lets you download a list of filenames generated using a pattern. IDM does this. There's probably others.