The high-level answer to this is "whatever you want for your campaign," but if you want more specific ideas:
If you use a spiritual gateway
The primary clues left behind would be gleaned from the local spirits. Not all spirits have the ability to pierce the Gauntlet on their own, so a large number of spirits in Twilight would indicate that those spirits were let across by some sort of gateway.
Ghosts in the Shadow would be a clear sign of such. Additionally, the motes generated by the abduction would lead to some odd spirits: spirits of abduction, of transition, of fear, of invasion.
Of course, since a Shadow gateway lets through anyone, finding the player's pet dog or the building superintendent in the local spirit world (possessed, Claimed, or starved to death, depending on how long it's been) would be an immediate and obvious clue. Having the material being get Claimed and cross back over would even give them a unique witness to interview.
If you use an occult matrix
Your primary clues are going to be along the lines of glitches in reality. The God-Machine is powerful, but it doesn't care about leaving evidence behind. All the clocks in the building stopped at the time of abduction, the victim's VHS tapes all overwritten with a staticky image of a door in the middle of his bedroom, or the fibers of his carpet being reoriented into a circuit-like crop-circle pattern. It could be something as simple and unsettling as all the dust in the room being slightly attracted to the abduction point, leading to an inexplicable pile of dust bunnies at the spot of departure.
The angel could have taken physical form, leaving behind physical evidence: feathers, a dusting of tiny sequin-like gears, the enduring scent of lemongrass and twine. The victim could have left mundane signs of disappearance like scratches where he tried to hold on to something or things knocked over in the struggle.
Finally, remember that an occult matrix takes work to set up. The abduction may be the result of an occult matrix, but the God-Machine's agents had to do something to make it happen. Did they have to mark a path in chalk from the nearest power substation to the victim's front door? Did they strangle 144 pigeons and arrange them in an elaborate pattern on his roof? Did they involve him in a complex Nigerian scam email thread that involved him sharing his address, blood type, and greatest fear? You can figure out the Infrastructure required for the occult matrix and decide what's left behind for the players to find.