IIRC during the first months of the pandemic most deaths showed a pattern where, from onset of symptoms, the disease would be unpleasant for ~7 days then the patient would seem to recover, and then suddenly worsen around day 10-14. New cases were typically detected around onset of symptoms, so I'd guess that's where we get the general assumption that deaths will trail new cases by 2 weeks.

I'd be curious whether we're detecting noticeably earlier than symptoms now, in countries like Australia with very proactive testing and contact tracing.