A gym membership and storage unit are much cheaper than rent. The storage unit provides a secure place to keep the shit you can’t carry with you. And the gym provides 24 hour access to showers, lockers, clean drinking water, physical activity, and potentially even socialization in fitness classes. If you get a membership for a big chain gym, you could likely even travel around and simply stop wherever the local gym is.
The local library is free, and you can exist there all day as long as you’re not sleeping or causing a disturbance. They probably have classes and meet groups for things you’re interested in, so you can stay social. You can charge your devices at the library while you’re there, so you can keep your phone/laptop/portable battery bank/etc working. In most cases, you don’t even need a library card to hang out and read in the library. You’d only need a card for checking things out.
You could likely even work from a laptop while at the library, to keep the gym membership and food paid for. Transcription jobs are easy to find on a freelance basis, and only require a laptop with Internet access.
This pretty much leaves overnight shelter. And depending on where you live, (local climate, friendly management that doesn’t harass you for staying in their parking lot, etc) the overnight shelter may be manageable with a car. You could potentially exist indefinitely without a traditional form of shelter (like an apartment or house) as long as you’re able to reliably sleep in your car or have a safe place for a tent.
But a lack of food and clean water will kill you in hours or days. And a lack of hygiene will quickly make it impossible to exist in society without immediately standing out. Lack of hygiene will also impact your mental health drastically, as discomfort and stink quickly becomes a nagging, omnipresent feeling. And the ostracism from being unhygienic is hard to come back from.
Drink lots of water and refill your bottle whenever you can. Shower regularly, so your clothes stay clean longer. Wash your clothes as regularly as you can afford. Avoid sliding into filth, because existing in society while homeless is infinitely harder when people immediately recognize you as homeless. Your goal is to blend in, and that requires a baseline of cleanliness and being able to socialize.