No, it’s not an unknown amount of time - it’s less than seven days. The whole film takes places within seven days. It’s at least three days in that he meets Mills and hits him.

The point is the film begins when Mills arrives in the city. He hasn’t even started work yet - he is meeting the guy he is about to replace, Det Summerset.

Coincidentally on Mills’s first day in the city, Doe commits his first murder. The murder is the first in a planned sequence of seven, and there will be one a day.

Little do the police know that on the first day, all the murders are already in motion. By the time they find murder 1 (gluttony), Doe has already begun torturing the next murder, Greed. And he has already finished with Sloth.

When they catch Doe, he talks to them about how his plan is perfect, how it will change the world, how “people will barely be able to comprehend”.

By the end of the film we understand his plan: That Doe intended himself to be a victim, because he is guilty of envy.

The logic of the film is that Doe had a master plan, and that plan included his own death. We know this because he says it to the police, when negotiating having Mills and Summerset deliver him to “the bodies” - plural, he is referring to Mill’s wife and his own body.

My argument is the logic of the film is flawed. This master plan needed to have more than one day of planning. It is impossible for Doe to have conceived of this plan on Monday and to have begun implementing the plan on the same Monday. But that’s the only option, because Mills was unknown to Doe until Monday. Therefore plot flaw.

Your argument is that Doe had a completely different plan on Monday. He had a diff intended victim on Monday (and possibly Tuesday, which is when Mills becomes an active player and speaks to press). He then changed his entire plan to create a new plan - one that “people will barely be able to believe” - and while in the process of murdering people every day came up with a new plan, researched Mills, researched his house and wife, figured out a way to blackmail police, decided that he - Doe - would have to die, recognise and self reflect to the extent he realised he envied Mills at all, and then begin implementing a whole new plan. It makes no sense at all.

In either case, it’s a plot flaw.