Variable thrust through changing the number of engines burning, or through propellant throttling, or other means is often/usually done to reduce maximum aerodynamic stresses on the rocket as well as to reduce maximum g-force experienced by the payload, which is sometimes human.
Question: Has an object ever been put into Earth orbit by a rocket where the first stage was always running at maximum thrust?
Ignore small variations in thrust due to Isp sensitivity to atmospheric pressure, maximum should mean maximum at that pressure.
Ideally, for the purposes of this question, it would be a rocket without boosters, since boosters running out of propellant is one way to reduce thrust.
Also, I won't rule out a whole class of propellants, but tuning the 3D structure and composition of a solid propellant (for solid or hybrid engines) could be tuned to produce a modulated thrust, and so a solid propellant 1st stage which lowers thrust to reduce maximum aerodynamic stresses should be ruled out as well.
note: I'm not asking if it would be a good idea to do so. I'm guessing that not all rockets always had provisions for variable thrust, or for shutting down engines sequentially.