That sequence was indeed not realistic. It's interesting to keep in mind that according to Expanse-lore, the Epstein drive on human-rated vessels operates typically around 11G. It is likely that a missle that is much lighter, so the rocket equation has less teeth, and not constrained by fragile meat-bag-physics, would be even more powerfull.

But if we just assume 11G, and constant acceleration (remember, specific impulse is supposed to be 1,100,000 seconds), that gets you to 0.05c in 37 hours. At that point, 8 lightminutes (1 AU) takes for example 160 minutes to travel. Not instantanious by any means, but a lot faster than one would imagine.

I’d argue that it’s just an effect of lazy writing though. Deorbiting anything into the sun is a very expensive way to get rid of it. They showed instant proto molecule cleanup operations in another season - just use that again.