Long story short: Cassie studied how much of Pompeii was excavated, all the way far into the future... and then buried the time machine schematics in town one day before the eruption of Mt. Vesuvius.
TRANSCRIPTION COURTESY OF JOSEPH HOUK - (KS) "Alright, then… So now there's just the small matter of getting the time machine schematics to us." (CW) "No problem. I'll be back in a second!" (KS) "So Cassie hid the schematics somewhere in this building?" [assuming the Pentagon] (MG) "Umm… No… To quote Doc Brown, 'You're not thinking fourth-dimensionally.'" (BG) "Cassie could leave here, fly to wherever she hid the schematics, then go back to whenever she hid them, retrieve them, maybe stay at a hotel somewhere, then fly back and timewarp back to a few seconds after when she left here." (KS, confused with the rest of us) "Ah… okay." (BG) "See? She's back already!" (MG) "Hey… Nice getup!" (CW, dressed as an ancient Roman woman) "Thanks. I'm glad they never got everything dug up in Pompeii…"