I remember reading a short story that featured settlements on Venus, and it mentioned the difficulty of running any sort of engine - rocket or combustion - on the surface. After all, your engine and its exhaust must be hotter than the atmosphere surrounding it, otherwise you're not running an engine, you're running a refridgerator.
I don't know if a rocket exhaust must absolutely be hotter than the environment, just at a higher pressure. If you open a gas bottle, the jet is going to be very cold, but it will produce thrust. With some quick googling, the surface pressure on venus is 90 bar, and a spacex falcon produces 350 bar in the chamber, so I think a falcon 9 could quite easily take off from the surface (ignoring the fact it would melt and the tanks might crush etc)
I don't doubt it's extremely challenging. But the initial engine temperature would still match the environment temperature, and it would not get somehow colder. That's not how any of this works.
