They didn’t need Lina Thum to estimate the time of death. Emily had been alive and well yesterday.
So it was less then 24hrs since she was last seen by anyone. That’s a not a lot of time to kill a woman, drain her of all bodily fluids, get to get work with her van I assume. Get her post death posed body into the place, and clean the place from top to bottom. It’s impossible without someone seeing you it has to be.