Did the first shot of Alice take place AFTER the events of the film?

Someone posed this fantastic question in another thread, where it was buried. I think it's worth more discussion.

Here's what I replied in the other thread:

Hmm. Interesting.
It hadn't occurred to me before, but it's certainly possible.

The way that the music is playing from the very first scene throws you off, because its continuity right up until he shuts off the player suggests that it's supposed to all be in realtime. But of course, that may not be the case.

The tennis rackets to me just seemed emblematic of their social class.

In the initial scene, she's not wearing any panties, but by the bathroom scene, she is. Hmmm.

The alcove does change though, as someone mentioned.
In the initial scene, there's nothing on the window sill, but in the scene where he's looking for his wallet, there are a bunch of pictures and doodads on the sill. In the initial scene, there are just the tennis rackets and a floorlamp in the left corner, but in the scene where he's looking for his wallet, the lamp is gone and it looks like a cloak or something is bunched up or hanging on something in that corner. In the initial scene, there's a throw rug in the middle of the floor, but in the scene where he's looking for his wallet, it's not there.
The camera is also placed differently. In the scene where he's looking for his wallet, the bookcase is very visible on the right, but in the initial scene, you can't see the right wall at all, whether by looking directly to the right or by looking for the reflection in the mirrors on the left. So it leaves an open question as to whether it really is the same room.

On the other hand, I just noticed that in the initial scene, the only shoes on the floor appear to be her shoes. None of his. But in the subsequent scene, both of their shoes are there. (The shoes are important because it wouldn't make sense for them to have two different rooms in the apartment with lots of shoes by the window, which means that it's probably the same room. The fact that so many objects have changed strongly suggests that the scenes are taking place at different times. Maybe they did split up and she got the apartment.)