Having progressed a lot further in my rewatch of Serial Experiments Lain, it seems that the "correct" answer is along the lines of the comment by user1306322. At the beginning of most episodes (with the exception of 10, 11, and 13), someone says a few short lines, such as the one above, or such as:
You've heard of a girl named Lain, right? Lain of the Wired. (Episode 3)
I don't need parents. Humans are all alone. They are not connected to anyone else at all. (Episode 4)
If you want to be free of suffering, you should believe in God. Whether or not you believe in Him, God is always by your side.
An exception is in episode 12, where there seems to be an exchange instead between what seems to be Lain and possibly either her mother or the doll figure she was addressing a couple episodes earlier.
Given this and the fact that the question at the opening of the first episode is somewhat similar to those "opening lines" in later episodes, it seems most reasonable to conclude that the question in the beginning of the first episode is meant to set the atmosphere, and that the addressee of the question is, as pointed out by the comment, anyone who hears it (the viewer, people in the Wired, Lain, etc.).
I still can't quite identify the speaker of the question in the beginning of the first episode, but it seems worth noting that the speaker of the "opening lines" seems to vary by episode. (I'm not completely sure about this since this could well be the same voice actress/character speaking the lines, but with a different inflection).