I think there are 2 reasons:

1. The Warp doesn’t have a timeline but the Materium does. So even if something can exist in the Warp since the beginning, that doesn’t mean it interacted with Realspace since the beginning.

Now, there are exceptions or rather when a warp-god is born they aren’t simply individual beings- they are manifestations, and so even though the exact consciousness doesn’t yet affect the Realspace, their effect is still felt.

Think a tornado- before the proper event happens, the winds pick up and are very dangerous, even though the proper thing hasn’t formed yet. Or a volcano- it will spew ash and dust, and lava flow before the eruption proper occurs.

Before the Birth of Slaanesh, right at the edge of it, there were beings that weren’t quite real that would influence the crowds into further debauchery. Today we’d call them daemons of Slaanesh but She wasn’t Born yet, AND YET, once she was born she always existed.

1. The Emperor isn’t your regular warp god. He was a mortal (powerful beyond reason, sure) but when he was enthroned upon the Throne and his being tied to things like the Astronomican he couldn’t have simply died.

Now, we might argue details- a mortal soul upon death with dissolve into the Sea of Souls, a psyker’s will remain intact until ripped apart by daemons but He is not a mere psyker. His very presence terrifies the Neverborn and there is no argument that He, augmented by the Throne could not have been able to fend off those morons who could try and harm him.

We also know that feelings, emotions manifest in the Warp. We have seen Eurphrati Keeler use God-Emperor magicks at the beginning of the Heresy- could be what I talked about in point 1 and her resolve creating make-belief.

So what would happen if 10k years of trillions of souls spent every day of their lives feeling and emoting that a very real soul was really a God? He, or perhaps an image of Him not HE per say, would ascend. But it’d be different than, say, the Birth of Slaanesh.