[citation needed]
primates don't spend the majority of their day gathering food; there's not reason to believe early humans were different.
I said, "majority of the day focused on gathering food, not "spent gathering food". If this seems like an arbitrary distinction, allow me to provide an analogy. Most teenage boys spend the majority of their day focused on having sex, but very few of them spend the majority of their day actually having sex (if they're even having sex at all).
As for a citation, ask anyone who's spent any amount of their life with not enough food available. If you ask them how much of their time is spent focused on getting food or thinking about food, or worrying about food, they'll probably tell you "most of it".
It certainly depends much on the regional setting. Humans pushed to the boundaries of landscapes which support their existence. If you are a hunter gatherer in fertile jungle setting you might make do with 2 or 3h per day of hunting or gathering. If you live further north or south or in more arid regions that might take more time.
Have you ever considered that this may be due to the fact that our brains evolved to exist in a world where our day is largely focused on gathering food? We're not well-equipped to exist in other modes.