How can I insert element into beginning of vector?

Use the std::vector::insert function accepting an iterator to the first element as a target position (iterator before which to insert the element):

#include <vector>

int main() {
    std::vector<int> v{ 1, 2, 3, 4, 5 };
    v.insert(v.begin(), 6);
}

Alternatively, append the element and perform the rotation to the right:

#include <vector>
#include <algorithm>

int main() {
    std::vector<int> v{ 1, 2, 3, 4, 5 };
    v.push_back(6);
    std::rotate(v.rbegin(), v.rbegin() + 1, v.rend());
}