A workaround I've thought of but not tested for matches in progress or finished is to look at the start times for the games on board one. If they match, that's the time. If they don't, take the earlier as it was probably a "one game at a time" not "two concurrent games" match.
bug: start_time missing from some matches

*bump*
While I have a workaround, this does appear to be a bug. Obviously not critically urgent to fix, but is there a ticket for it (or your equivalent in your bug tracking system?)

@skelos This issue should have been ticketed and, hopefully, resolved the 05/Feb/18 . I had a note to update this thread but actually it doesn't look so.
I've checked the links provided and all have a starting date, please confirm that it solved your problem.

Thanks Andrea. Of my links above all have start times, but of course #1 is now "in_progress" rather than registration.
Consider it fixed, and I'll open a new thread if I come across it again.
(I'd say "let me see" if I were working on matches at the moment, but I'm not. Next time I am and am touching my match code I'll take my workaround for "in_progress" and "finished" matches out, but I don't know when that will be. So "closed" is the right state for the ticket.)
Thanks again!
The start_time is missing from some matches. It is documented for all three match states: registration, in_progress and finished:
Example 1, registration state, Auto Start No, no end_time (correct) and no start_time (incorrect)
https://www.chess.com/club/matches/black-stone/869846
https://api.chess.com/pub/match/869846
Example 2, finished state, Auto Start Yes, has end_time but not start_time:
https://www.chess.com/club/matches/black-stone/719632
https://api.chess.com/pub/match/719632
Example 3, finished state, Auto Start Yes, has end_time but not start_time:
https://www.chess.com/club/matches/black-stone/821492
https://api.chess.com/pub/match/821492
I can't spot a pattern: both old matches and new matches have the problem, but not all do.
Of Black Stone's matches, 39 are missing their start_time and 198 have it present.