If you want to avoid tooth infections, the #1 thing you can do is stop eating sugary food / drinking alcohol or sugar water; for a more complete caveman approach, cut back on other starchy foods like rice, bread, and pasta. The #2 thing you can do is occasionally visit the dentist for a checkup or whenever your teeth give you trouble. The #3 thing you can do is occasionally apply topical fluoride (it’s not clear what difference there is between drinking fluoridated water, brushing weekly, brushing daily, ...). Getting a nutritious diet is also probably important.

Our modern culture taboos anything less than brushing multiple times per day, but it’s not clear how reliable the evidence is supporting this as a blanket requirement (the studies I’ve seen had many other confounding variables, but admittedly I did not do an exhaustive literature review), and most of the tooth infections probably result from other causes.

There are people with perfect teeth who brush rarely, and people with frequent caries who brush religiously after every meal. On average, hunter–gatherers have better teeth than people in agricultural societies, including modern ones. They don’t have access to oral surgery, so when things go bad they can go very bad. But that’s not really related to brushing.