Not really, my first car, a 1950 Mercury had push button start, but to actuate the button you needed to turn the ignition on with a key. I remember my dad's 1948 Nash having the starter button under the clutch pedal. I think most cars adopted ignition keys sometime in the late 1930s. I think the first car to use the ignition key to actually start the engine was the 1949 Chrysler.
My car, a Lexus ISF, has push button start. It's really very handy not having to pull the keys out of my pocket to unlock the doors and startup the car. Unlike my truck. Pull out the keys to activate the remote and then insert the key to start. Push button much more convenient.
Lou