Nip the bud
The air in the year 2001 feels the same as twenty years in the future, and the grass is as green with spots of yellow as I remember, and the sky isn't any bluer, either. All the old men lied!
This is the time soon after the White Castle reappeared in our dimension. I don't know what would happen if I and Zeke went farther into the past. My intuition says that there's nothing pleasant out there. Nothing pleasant at all.
But this is the earliest that the Time Eater could've started kidnapping people. At least, this is what we assume it's doing. The creature's species didn't exhibit any abilities to lure people towards them like sirens. The Time Eater itself used only its uncanny knowledge of time and alchemical devices that he must've scrounged from Istvan's laboratory.