In evolutionary terms, I risk we can see it the other way around.
Our ancestors started as herbivores, being tree dwellers, and only later changed into the role of scavenger and after that predator, making the consumption of other animals a viable and reliable food source.
The species evolved into the role of the omnivore, capable of eating nearly anything to survive, and it proved to be a winning strategy.
If the concern is the apport of B12, eggs are a source for it and it would be an easy enough one for early humans to get it.