I am doing my absolute darndest to not purchase anything new, whenever possible. Although I'm still in the early phase, I have a couple of tips/tricks I can share based on my experience:
1) Time is your friend. The more time you allow yourself, the less likely you are to have to pay for something new. The faster things need to be done, the more it will cost, because you'll need to get those materials now, instead of continuing to keep your eyes peeled for the right thing.
2) Start looking for it before you need it. I have never found what I was looking for at a thrift store when I needed it, but by hitting the thrift store once per month, I always find something I know I will use. For example, I got a nice sweatshirt on a really hot summer day.
To make this work for your project, start thinking a phase or two ahead. That way you can jump on opportunities and have materials ready before you need them. (See tip #1)
3) It helps to have space for staging the materials you will be using in the future. The more space you can set aside, the more advance gathering you can do. I have found incredible materials for free, that I'm not quite sure if they will work out for the project. By having the space, I can say yes and not consternate as much about whether I really need that much of this type of board or widget, or if it is the perfect dimension, etc...
4) Technology is a game changer. If you have a smart phone, download a craigslist app and set searches for the things you need. It'll let opportunities come to you and you can jump on them. Same with FB Marketplace.
5) Make a point of popping in on some local sources of stuff, every week or so (see #2). For example, I try to pop in on my local Habitat for Humanity Re-store and landfill recovery center every week or two. When I hit later phases, I plan to hit more thrift stores and garage sales, etc...
6) I don't have one near me, but I'd try to find the closest RV junk yard to you. They are a great source of materials you'll want and need.
7) Upcycle! Sometimes a little labor is what you'll need to make the materials you find work for you. I have had searches set for insulation for quite some time. I have gotten very inexpensive havelock wool and free denim insulation, but I'm not finding foam boards that I want for the walls. I decided that I will make foam wall boards by taking clean foam from a furniture store dumpsters. To make the foam the shape I want, I have learned to make a simple hot wire foam knife and jig to cut it to the thickness I need without the mess. My plan is to glue it onto a radiant barrier material and make sheets. I dunno, might not work, but I enjoy the creative process!
Hope there's something in my approach that is helpful to you!