C++ "new operator" as a factory?

I try to use the "new" operator to instanciate a specific class and not the one behind the "new" keyword.

I try to have a kind of "factory" for an abstract class.

It seems to me that it is not possible, but lets double check ! This code compile, but the main code treat it as a "Test" (and not a TestImpl" class)

class Test
{
public:
  virtual int testCall() { return 0; };

  static void* operator new(std::size_t);
};

class TestImpl : public Test
{
  virtual int testCall() override
  {
    return i;
  }

  int i = 15;
};

void* Test::operator new(size_t sz)
{
  return ::new TestImpl();
}

void main()
{
  Test * t = new Test(); // Call the new operator, correctly
  int i = test->testCall(); // i == 0 and not 15
}