The Future Can Not Be Deduced.
Omniscience cannot be the end product of any intellect that could meaningfully communicate with our kind of life.
There are hard limits to the amount of knowledge one can have about the state of a system. Hard limits to the accuracy of any model. Non determinism is baked into any description of the universe.
Consider just a few examples:
The n-body problem.
Boltzmann's statistical mechanics.
The ideal gas law.
The second law of thermodynamics.
Quantum electrodynamics, which perfectly marries theory and experiment.
The laws of motion, in general rapidly become non linear, even though ballistics is something we've mastered.
All of these discoveries are powerful and rigorously tested arguments against omniscience. No matter how powerful the intellect, what it cannot do is stand in a frame of reference and predict the future.
Back To The Future
Now, I recall reading decades ago something about Maxwell's wave equations being time invariant, so any EM transmitter broadcasts into the past as well as the future, except 180 degrees out of phase, so tomorrow's news would be cancelled out, or something like that.
EDIT: Decoherence is the term used for the time invariance of quantum mechanics, apparently. Seems like the Observer negates this at this level. I don't think this will help, the only force we can grow a nose for is electromagnetic.
The point was that lots of physics works perfectly well both ways in time, assuming 2 dimensional time. All bets are off if time is multidimensional. Since we should be calling it spacetime, this is almost certainly the case.
The Broken Symmetries of the Mexican Hat Dance
There is a thing called symmetry breaking which might explain these things. The canonical example is a marble on a sombrero. This is symmetrical. We don't see this a lot, because the symmetry state is not the stable state. The stable state is the marble on the brim. Not symmetrical. This system under stress will go from symmetry to asymmetry. AKA symmetry breaking. If you happen upon this system, most likely you'd not view it as a symmetrical system, although that is exactly what it was. Here's a better explanation.
So we have a couple of asymmetries in our observed world.
Where is all the antimatter?
Why do we see time go one way, when much of our math works perfectly fine both ways?
Seems to me that work on the antimatter problem might, as is so often the case, stumble upon something totally unexpected. In this case a way to interpret EM waves moving backwards in time. The link would be the symmetries and the math needed to explore them. You'd need to build something to detect whatever your math told you might be there. This is how we found the background microwave emissions. Looking for something else completely, built a detector, oh dang, it's noisy, oh wait! turned out that the noise was actually significant.
A backward linear projection of this event along your time axis would be equivalent to you bouncing light off of a future object. You'd amplify this, clean up the noise, put it on a monitor and that would be a flatlander's view of the future. It would not be completely accurate, so you'd triangulate ( just like you would with any other EM source ).
The Birds and The Bees
So: We have light from the future. "Future light" or something similar. This is now a biology problem. Snakes use infrared to hunt. Bees use UV to navigate. Birds sense magnetism. Sharks use electricity to find prey. Some few humans might have the ability to sense, feel, taste, whatever this "Future light." ( Snakes taste infrared, using their tongue. ) Perhaps it manifests as an ability to interpret the images intuitively. Maybe it's like a test for colour blindness, that 99.9% of people fail, but a few say "No, that's a picture of your dad, getting an award." ( It's you! Congrats! )
Find 3 of these people, or breed them, and you'll have a way to triangulate future events biologically. It comes out of research into broken symmetries, matter vs antimatter, or matter vs dark matter, assuming dark matter is actually a thing and not just a vast but understandable reluctance to junk a whole bunch of theory that works perfectly. It would not be the first time, or even the second. Even great minds are not above fudging the equations.
Keep in mind however, that this is literally foreshadowing. You'd need to use this light to make a hologram or some other 3D representation, math might help, but you and your seers still live in Flatland.
These people would have existed for all of human history, except the triangulation is the key, right? Something good or bad is always about to happen, this is why Cassandra was ridiculed. Nope, what you need is at least 3 of these people to get actionable data on the future, to triangulate a projection for study, interpret it, and then you have to trust that they are not projecting their thoughts and desires into the image. Also, gobs and gobs of processing power. You know, like say..
So looks like it's a mutation carried by XX humans, which is also your precogs in Minority Report. Really, for your story, these women should be drifting towards the lab for a variety of vague reasons.
Oh, they'd probably present with synesthesia, because there could be a variety of ways to map this "Future Light" onto whatever system detects it. The point is that it's a kind of light, light that has been around forever, and a formerly useless mutation might be able to detect it.