Your question brought to mind a story I think about often. A bunch of years ago, my sister married a really great guy from Norway. He had some buddies who were in the wedding, who had never been to the States but were really into rock climbing, mountaineering, and Metallica. So these two crazy Norwegians flew into LAX with their backpacking gear, their climbing racks, and a few thousand dollars. First day in the country they bought a $3000 minivan, a cooler and some food from BigBox, loaded up, and set out across the country. They spent a few months driving from LA to Joshua Tree, up through Yosemite, down through Vegas/Red Rocks, down to the Hueco Tanks, up through the Smokies, then up Skyline Drive, further north to the mountains in New Hampshire, and then down to south eastern VA. They saw Metallica three or four times on that trip, climbed most of the best areas in the US, did a ton of dispersed camping, and then sold the van for what they paid for it before flying home.
Those guys did more overlanding, I'd bet, for a few grand in parts from Advanced Auto, a Tractor Supply tool kit, and a case of Slim Jims than most full builds will ever do. Not that theirs is the only way, or even the best way. (It was really good they had access to a shower before the wedding.) But, if you want to go get it, it doesn't take a ton of money, and I can't think of anyone who would say their trip wasn't "real overlanding" though we called it dirtbagging back then.
TLDR: get out there and see the country. It'll be an adventure no matter how you do it.