The simplest way to get the multiplication to happen in an unsigned type that is at least uint32_t, and also at least unsigned int, is to involve an expression of type unsigned int.
v = 1U * s1 * s2;
This either converts 1U to uint32_t, or s1 and s2 to unsigned int, depending on what’s appropriate for your particular platform.
@Deduplicator comments that some compilers, where uint32_t is narrower than unsigned int, may warn about the implicit conversion in the assignment, and notes that such warnings are likely suppressable by making the conversion explicit:
v = (uint32_t) (1U * s1 * S2);
It looks a bit less elegant, in my opinion, though.