Is it possible to defer member variable initialization to inherited class without modifying the parent class?

I'm having a specific problem which I've converted into the following Minimal, Complete, and Verifiable example.

#include <iostream>

class Foo {
    public:
        Foo(int v) : val(v) {}

        int get_val() const
        {
            return val;
        }

    private:
        int val;
};

class Parent {
    public:
        Parent() : member(0) {}

        const Foo& get_member() const
        {
            return member;
        }

    protected:
        Foo member;
};

// Nothing above this line should be changed

class Child : public Parent
{
    public:
        // This doesn't work (compile error)
        //Child() Parent::member(1) {}

        // Nor does this (also a compile error)
        //Child() this->member(1) {}
};

int main()
{
    Child x;
    std::cout << x.get_member().get_val() << std::endl;
    return 0;
}

This example demonstrates the issue I'm having in a larger software project where I'm inheriting from an external library but need to directly initialize one of the parent's member variables.

Unfortunately, the Parent class does not have a constructor which parameterizes its member's initialization.

If the Parent class had a constructor of the form

Parent(int val) : member(val) {}

then I could write a Child constructor as

Child() Parent::Parent(1) {}

but that is not the case for me.

Question: Is it possible to defer the initialization of a parent's member variable to an inherited class? If so, how?