It's possible to allocate a large amount of memory from the stack in main() and have your code sub-allocate it later on. It's a silly thing to do since it means your program is taking up memory that it doesn't actually need.
I can think of no reason (save some kind of silly programming challenge or learning exercise) for wanting to avoid the heap. If you've "heard" that heap allocation is slow and stack allocation is fast, it's simply because the heap involves dynamic allocation. If you were to dynamically allocate memory from a reserved block within the stack, it would be just as slow.
Stack allocation is easy and fast because you may only deallocate the "youngest" item on the stack. It works for local variables. It doesn't work for dynamic data structures.
Edit: Having seen the motivation for the question...
Firstly, the heap and the stack have to compete for the same amount of available space. Generally, they grow towards each other. This means that if you move all your heap usage into the stack somehow, then rather than stack colliding with heap, the stack size will just exceed the amount of RAM you have available.
I think you just need to watch your heap and stack usage (you can grab pointers to local variables to get an idea of where the stack is at the moment) and if it's too high, reduce it. If you have lots of small dynamically-allocated objects, remember that each allocation has some memory overhead, so sub-allocating them from a pool can help cut down on memory requirements. If you use recursion anywhere think about replacing it with an array-based solution.