No.
https://en.wikipedia.org/wiki/Pleistocene_human_diet
tldr: Homo habilis ate some meat, and Homo erectus was more of an omnivore, eating tougher-to-chew/digest foods...and even later, started to cook foods...both meat and plant-based.
The "paleo" diet is what happens when a bunch of jocks get high, watch the Flintstones and decide to base a diet off what they saw.