I'm breaking my brain for a two weeks trying to find a way to build a fireproof box 100 cm × 100 cm × 100 cm with 1 door at the cheapest price.
I'm looking for an idea.
First, you need a better specification than "fireproof." Is the objective to build a box that survives a flame for a certain time? Is it to protect the contents? Does the box need to keep people out or things in? Be specific.
Fireproof items will be typically built with some type of clay-ish fire brick. Depending on how long and how hot the fire needs to be, you might be able to get away with common building bricks with an internal support. If not, manufactured fire brick will almost always be the best choice.
If the problem were to just make a box that itself did not burn in an housefire, that seems trivial and somewhat useless - 100 cm cube of brick that holds 0 (pick your volumetric units) contents
If the goal is to protect the contents from a fire you have to understand that many items one wants to protect would deterioriate with heat.
Even the best insulation (probably aerogel) can only buy you time. If it takes half an hour for the inside of my box to reach 100 degrees in a 500 degree fire, I just need to keep the fire on it longer and eventually I can get the contents to hit pretty close to the 500 degrees.
If you use a more active solution such as a compound that will absorb heat, possibly releasing a relatively inert gas that will pressurize the box so that flames flow away rather than in, cost will go up and it will still only last as long as your chemical anti-fuel. On top of it, you will have to maintain the compound, and prevent it from exploding from thermal shocks of the fire (adding another layer to the problem).
Also fyi, it is possible to spot and seam weld extremely thin metal sheets if the process conditions are appropriately controlled. Anyway, I suspect you will end up with a 22ga spot welded box, 'sealed' with ceramic adhesive or braze and lined with insulation. "Keeps your stuff at Xdegrees or below for a whole Y hours in a Zdegree fire. (Only tested for fires from A - Trash, wood, paper. C - Electrical equipment)"
The main problems is the size. At that size, you might as well build it using brick if you want it fireproof and at a low cost.
Having 1.5 mm metal thickness is too small for welding and to structurally support any load. Even at 1.5[mm] thickness the weight will be at least 70 kg, so practically it will be immovable. If you double the thickness (which I think is the minimum), then its going to be 140[kg]...
Look up DIY forge ideas... the principal works the same, but in reverse. They use materials to insulate a Firebox to hold the heat in so they can melt metal. Would work the same to insulate items you don't want to get hot. I think your garden supply perlite mixture with a plaster Paris or some kind of fire mortar would probably be a safe bet. I would also look into getting your hands on some fiberglass fibers to add to the mixture. Shredded fiberglass strands are added to concrete mixtures to mitigate potential cracking. Also, keep in mind that generally when one makes a box, they are also trying to make it water resistant for when the firefighters come to put out the fire it doesn't ruin the documents. You could literally build the box out of anything because it would mainly just be a mold.
