BPS.space is attempting it.
Test Launch: https://www.youtube.com/watch?v=QQt-9SSJ51c
Test Landing: https://www.youtube.com/watch?v=lXy-x6lkQvQ
Test Launch: https://www.youtube.com/watch?v=QQt-9SSJ51c
Test Landing: https://www.youtube.com/watch?v=lXy-x6lkQvQ
This appears to be working with solid rocket motors, thrust vectoring, and a carefully timed ignition. How do they get accurate distance to ground? Is altitude just a constant for these tests?
I wonder what scale you would need to get the rocket into space/orbit? SpaceX should fund this guy to find out, could prove to be a valuable bootcamp for real SpaceX employees in the future?
There's a great "what if" xkcd about using solid fuel model rocket engines (the same type used in BPS.space's rockets) to get to space and orbit.
The summary is that you may be able to use a stupendously large number of them to get to space, but orbit is physically impossible. You'll need a different propulsion method.
The smallest rocket that has ever carried a payload to orbit is the SS-520. It's ~30 feet tall, ~2 feet in diameter and weighs ~5,700 pounds. It set the record in February 2018, so it's a pretty recent record.