Getting into orbit is more about horizontal speed than altitude.
The bigger the nozzle the faster the exhaust gas. Efficiency is proportional to the square of the speed of the exhaust gas.
The bigger the nozzle the lower the pressure of the exhaust gas. If the nozzle is too big then the atmospheric gas goes into the nozzle. That’s the limit on nozzle size for sea level launches.
Starting high is better because you can have a MUCH more efficient engine.