My method creates an std::map<int, int> and populates it with the number and its frequency by iterating over the array once, but I'm wondering if there's a quicker way without using a map.
std::unordered_map<int,int> can count frequencies as well but its operator[] has complexity (cppreference):
Average case: constant, worst case: linear in size.
Compared to
Logarithmic in the size of the container.
with a std::map.
When the maximum number is small you can use an array, and directly count:
for (const auto& number : array) counter[number]++;
Admittetly, all this has already been said in comments, so I'll also add this one: You need to measure. Complexity is only about asymptotic runtime, while for given input size a std::map can actually be faster.