Here's a really easy way to make a mat.
You'll need a roll of vinyl or any sort of plasticised material, the essential thing is that the material you use is compatible with the glue you use.
This is the clear vinyl I bought, just google for it or keep your eyes open when you're driving around as there are lots of small places that sell or use vinyl.
It's clear weatherproof sheet. And the glue is a certain vinyl glue too. Made in the U.S. But once again Google for it.
And you'll need a cleaner to prep the material that you're glueing and that is easily available from any hardware store.
And then just a roller to smooth the joins together.
And that's all the hardware you'll need. Sure you could buy or build a heat welding system but vinyl glues are used around the world for plumbing so it's tried and tested, the glue basically melts both surfaces and joins them together as one piece. Even thin joins are permanent and the material is going to fail before the join.
Now all you have to do is come up with a design to build....