There are things that drop straight down from 350km altitude: sounding rockets. These are sub-orbital rockets that go straight up to that altitude. The payload has a few minutes to perform measurements before it hits the atmosphere again. These payloads are equipped with simple heat shields and parachutes, and are nowhere near as elaborate as orbital space capsules.
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“It will go up like a cannonball, and come down like… a cannonball.” - von Braun in The Right Stuff
I believe it would do just fine from 0 speed at orbital altitude (with ref to the earth’s surface). A lot of the launch abort scenarios involve return to Kennedy or Europe after engine failures. They would get maneuvering speed just by dropping the nose with reaction thrusters, and wait for enough air to glide. Reaching a runway might be the biggest problem at that point…pack your chutes just in case.