My guess: the Witness is Dr. Elliot Jones, Katarina's ex. And Olivia is his and Jones's daughter Hannah, who Jones thinks is dead.
--Remember, Elliott CREATED the time machine. He of all the characters we've met, knows the most about time travel, more even than Jones. That makes him a prime candidate for being the Witness. He was even able to get Ramse a dose of the time-travel drug, way back in 2016 before the technology was fully developed.
--Peter Outerbridge's stature. He's a top-notch Canadian actor who has starred in numerous TV shows. Unlikely the showrunners brought someone so high-profile on for just a two-minute scene.
--Elliot's also linked to the red hallucinogenic herb which the Army and Jennifer use. Railly saw a whole room full of it in Raritan Laboratory; presumably this was created accidentally during Elliot's experiments, and he discovered its hallucinogenic properties later.
--Misdirection: He's super-deferential to Ramse in the scene where they appear together, bowing and scraping, so you don't think he could be the big bad. He's also depicted as an eccentric, geeky scientist, again, not the profile of the big bad.
--Olivia's references to her father are very negative. Elliot abandoned Jones when she got pregnant, so he's a lousy husband/father. Olivia said her father had plans for her; again, possibly meaning that Elliot had raised her to lead the Army. While speaking to the Witness in her vision, Olivia is angry and demands "What do you want from me?" If Elliot is the Witness and she's Hannah, then this scene makes sense.
--That Jones thinks Hannah's dead doesn't mean she actually is. Elliot could easily have brought her to another time and raised her without Jones's knowledge. Even if she'd had the plague, we know Col. Foster may have cured it.