I don’t know how there could be an “optimum” population. Optimum for whom? One could argue that the earth would be better off with no humans at all. Certainly more resources for fewer people is better than fewer resources for more.
That said, I think we can support more, but not too much more.
It took 200,000 years of human history to get to 1 billion; it took only 200 years to get from 1 billion to 7 billion.
Yeah, there’s empty space, but what about all the space needed for agriculture to feed those additional people and provide lumber to build housing for them? What about the fact that we can’t even feed all the people we have now for various reasons?
I don’t think we’ve exceeded it; I’m no “overpopulation” alarmist, but if the population continues to soar as it has for the past century, then we will exceed it soon.