You don't need $2,000.
You can survive with $0.
But you won't have the benefits of modernity.
Like modern medicine or science and technology.
This is just how the Indigenous man lived before colonization.
You can always get a place out in the country, with a steady income and a job.
Then you can enjoy being out in nature, while also enjoying things like hospitals and the internet and trucks and computers.
If you just want to get out in nature and backpack for a while, for weeks, for months, then get a solid pack, like 50L or 100L pack.
Then you can pack a camp, a means to purify water, a weapon/traps for fishing and hunting, a tool like an axe for building shelter.
This is how the Indigenous man lived, it's not far off from how a lot of rednecks live up here, and people on reservation land.
You can even camp with just a tarp and no tent, or build your own shelter, like bushcraft or traditional shelters.
You can get away with stealth camping, but at some point, the ranger may catch on to you and confront you.
If you are on public land, the park ranger will be on your tail, and you will have to move a lot.
You have 14 days, two weeks, within a 28 day period to camp on public land.
If you want to just be a vagrant, then hop between different sites.
I've been homeless, just doing migrant labor, lived in a shelter though.
Living like a wild man is certainly doable, but you will miss civilization and you will need a woman some day.
If you refuse to leave and insist on living on God's green Earth in a traditional way, you will go to jail.
But not on reservation land. Just respect the environment, cleaning your traces hides your trail too.