How do I ask for “at least” a size of an int in C

The standard header stdint.h provides the types int_leastN_t and uint_leastN_t, where N is 8, 16, 32, and 64 (and possibly others, but these are not required). These are standard as of C99.

It also provides “fast” alternatives, aka int_fastN_t and uint_fastN_t, with the same values of N.

So, in your case, you can use int_least32_t or int_fast32_t.