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When rockets launch for orbit they travel up and the air thins respectively to the speed increasing.

How fast can a rocket for travel at sea level before it would fail or the elevation would have to rise?

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The Sprint missile could get up to 3 kilometers a second very briefly and with the outside shell going white hot.

https://en.wikipedia.org/wiki/Sprint_(missile)

That is approximately 1/3 orbital velocity or 1/4 earth escape velocity, depending on which one you meant.

Going faster will involve exponential increase in needed power to overcome drag. And dealing with the massive heat loads generated. The SR71 blackbird operated far higher altitudes at only ~900ms but is a useful example of a heat limited vehicle (cooling achieved by transferring heat into the jet fuel before burning),


GIF of visible light photography of a Sprint missile turning white hot from drag heating in the atmosphere, taken from Scott Manley's Shooting Down A Missile With Another Missile, In Space.

Sprint missile turning white hot

Frames show that each part of the missile briefly passes through red before turning white.

Sprint missile (just before) turning white hot

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