Perhaps not in the same sense that we usually feel happiness, but surely the feel it, after all happiness is a universal feeling that was not "invented" or "devised" in modern times.
And from just imagining what it was like to live in an era where concerns were mainly dominated by basic and primitive circumstances and needs like eating and surviving day by day, it is more than obvious to imagine that not only were they happy but they were sure lived a life in total freedom and with the greatest happiness that wildlife is capable of offering.
We will never know whether they were happy but I am pretty sure they were. Happiness is a form of emotion and emotions are normal. Even animals have emotions.
Today rich people in the US can be happy but also poor people e.g. in indonesia. It doesn't have something to do with wealth or physical ownership of things. That's why I think that they were happy, but still nobody will ever know.
I'm thinking they most likely were at times, because in our nature, we generally don't reproduce as efficiently when we are not happy. Considering the fact that we are still here, I think prehistoric people had less mental health problems.
I guess it is hard to figure out. I am not that good at history but I can't even imagine what kind of drawings could they have left us and how could we figure out if they were happy or not. I assume they didn't felt that happiness feeling too often because there wasn't much to do at that time other than hunt, survive and procreate. Probably during procreation they felt happy, but I guess their consciousness was limited at that time and their lives somehow were consumed on survival activities and not that much on activities that would make them happy and fulfill them. Nowadays we have much more factors do trigger happiness than during those times. I don't even know if they were able to talk. Overall happiness I don't think they had.