This reminds me of the Avatars series, by Tui T Sutherland. The first book is Avatars: So This is How It Ends, and there are at least three other books in the series: Shadow Falling, The Menagerie, and The Menagerie #2. The first book, at least the edition I saw, was published in 2006, so a couple years later than your time frame.
The basic plot-line has four teens wake up in a post apocalyptic world, about 75 years into their own future. Each kid discovers they now have magical powers, different ones per kid. Humankind is pretty scarce - kids had stopped being born, the only people left were old and knew there was no future generation (at least until teens pop up), and there were also robot monsters and bio-engineered animals running around.
The kids were brought forward in time because
the gods of the major (polytheistic) pantheons - Greek, Egyptian, Meso-American, Hindu, and Polynesian - had chosen the kids as avatars to fight out among themselves which pantheon would be the ultimate gods and have power over the others.
As far as I recall, each kid was a representation of a different historical people, and so were each of a different ethnicity. This would match the point that the kids all looked different.
People had stopped being born (leading to the post-apocalyptic world) because
Humanity was going to be restarted (I think) under the auspices of the winning pantheon - since they had all stopped believing in the gods, in modern times especially, wiping them out and starting over with a civilization completely under their thumb from the start was more convenient or something.
There was definitely an expectation (at least by the aged humans still alive) that the kids, being kids and "clearly" young enough to be from after the point where kids had stopped being born - or at least of reproducing age given that they're teenagers - and thus would somehow fix things and restore humanity. Obviously whether this happens or not is a plot point.
I recall a specific scene where there is a group that has a child, just one, who was born quite late after the cutoff point. The group had a semi-religious belief she was some sort of sign or savior that would restore humanity, even though they were not sure how (she was born incapable of reproduction, and the actual problem was no kids, so no obvious fix). Actually, the whole setup was a joke on one of the pantheon's parts, giving false hope for amusement.