C++ Complex initialization

I have a complex Parameters object, which I'd like to use to parse CLI arguments and which contains all relevant parameters for the rest of the program. I also would like the class to do some preprocessing, so it is directly constructing objects from the parameters for later use. Something like:

class Parameters {
    Parameters(int argc, char* argv[]);

    ComplexObject complexParameter;
    int parameter1;
    std::string parameter2;
    /* ... multiple parameters ... */
}

Parameters::Parameters(int argc, char* argv[]) {
   /* parsing in simple parameters using getopts and a long switch case structure*/

   complexParameter = ComplexObject(parameter1, parameter2 /*...*/);
}

The problem is, ComplexObject doesn't have a default constructor, but the constructor of Parameters requires me to initialize complexParameter (for example by using a initializer list). Initializing complexParameter with some stand-in values and later replacing it doesn't seem like a good solution to me, and I don't know how I would use a initializer list in this case.

What would be the best way to circumvent this? Should I use a factory method Parameters::create() where I construct a Parameters object using a really long constructor like

Parameters(parameter1, parameter2, /*...*/ ComplexObject(parameter1, parameter2))

at the end? Or should I put the construction of more complex objects in the main, or further compartimentalize my Parameters structure? Or should I use a (smart) pointer for ComplexObject? In the last case, I would need to create one with new and also take care of destruction of it, right? I just can't think of an easy solution. I guess I'm just not used to the fact that in C++ objects are not nullable. In other languages I'd just initiliaze it at the end of the constructor.