It’s equally possible that there was more than one or even a day where only people were born and no one died.
There was a low point where only about 2,000 humans were estimated to be alive. Certainly you couldn’t have had someone dying everyday then
If there was at least one, it also means there was a last day prior to today where no humans died, that went unnoticed and unremarked, and probably will be the last for a long time yet.