How does a 32-bit DSP address 2³² values without enough RAM?
Your question is based on two incorrect assumptions.

A 32-bit CPU is capable of addressing 2³² individual bytes, so it must include 2³² bytes of RAM.

Merely being able to address 2³² individual bytes does not require actually having 2³² bytes of RAM. To have address space of 2³², the CPU only needs to use 1 number (i.e. a 32-bit integer) to represent its memory address, one address at a time, not 2³² numbers simultaneously.
Also, a memory address don't necessarily map to an uniquely usable physical memory cell. It's perfectly possible to have a 32-bit computer with only 128 MiB of RAM installed. The remaining address space in this case can simply be unused. And in fact, a larger-than-physical-memory address space is still beneficial since it can be utilized to implement Memory-Mapped I/O and virtual memory, which use parts of the address space to represent something other than &quot;real&quot; physical memory.

An n-bit CPU must have an n-bit address space, and must support n-bit of physical RAM.

Usually, we assume a modern n-bit CPU that support n-bit integer arithmetic operations has an n-bit address space and support n-bit of physical RAM. But it isn't always the case. The Motorola 68000 is an interesting example - it supports 32-bit arithmetic operations, has a 32-bit address space, but only include a 24-bit physical address bus, and a 16-bit data bus. Is it a 16-bit CPU, a 24-bit CPU or a 32-bit CPU? It's thought to be 32-bit due to its capability of doing 32-bit arithmetic, and also considered to be 16-bit due to its data bus width. But both answers would be wrong if you expect the &quot;n-bit&quot; indicates the amount of physical memory supported by the CPU, which is 2²⁴ bytes. Going back further, many historical CPUs, such as the Intel 8080, support 2¹⁶ bytes of physical memory despite being 8-bit CPUs.
Thus, being considered as an n-bit CPU does not require actually having 2^n bytes of RAM, also, the &quot;n-bit&quot; does not even always imply the amount of physical memory supported by the CPU.