How does the memory allocator statically linked into the application request a new memory allocation into it's address space (sbrk or VirtualAlloc etc.)? Allocating memory will in most cases involve calling into the kernel, it's kinda a core function of a kernel. It has to have some link externally to the programme, directly or indirectly.

The smallest amount of memory you can request from the OS is a page (typically 4K, sometimes 16K), and there’s a lot of additional stuff that goes on in malloc().