More so the grim question: if you were in a typical space suit sitting in a ship just outside Jupiter, then propelled yourself towards the planet - what would kill you first?
Assume you are close enough that from the moment you are launched out, you are “in” the atmosphere at the outer edges. Also assume moving fast enough that the answer is not “dying from dehydration”.
I discussed a bit with GPT 4o and came to the conclusion that shear wind gusts of over 300mph in the upper atmosphere would probably do it. You’d hit that almost instantly, before high pressure, temperature or highly corrosive materials.