Tire and wheel combo dictates how low you can go. Tires vary a lot as well as wheels. If the wheel has a pronounced inner bead to help hold tire in place, and if the tire is thick or thin, stiff or soft, little, too many variables to say for sure. There is some sort of rule of thumb formula but I can’t remember it. You’d really need to blow one off a few times to know for sure. It also depends how hard you wheel. If you’re going straight through sand and need max float, you can go lower, but if you’re knocking up a rutted goat trail and slamming around, you might want higher pressure to keep the tire pushing back on hard knocks.
Tire type can make ride vary a lot! Lots of “mud tires” are designed for a wide range of vehicles including larger trucks, so they are often too heavy duty for small Suzuki. Generally the lighter a tire weighs the better it will handle off road, with the downsides of weight capacity and cut resistance etc.
also, the profile of the tire in relation to the wheel makes a huge difference. If you pull a wide tire in with a narrow wheel, it will ride softer over obstacles because the sidewall is not a straight up and down line. Narrow wheels with wide tires also help protect the wheel from rocks and curbs. But high speed handling can be worse as the tire rolls back and forth on the rim.
Having said all that, I think that football sized rocks are going to be noticed no matter what you drive.