Initialize object from unknown derived class of known base class

So, I'm making a library for a little D2D Engine; but that's not the point, the thing is, I have this class which will be the base class the user's class will inherit. My main idea would be something like this:

struct BaseEngine {
    // I have two pure virtual functions so the user has to define them.
    virtual bool onLoad() = 0;
    virtual bool onFrame() = 0;
};

Now, if it all were to be in the same project, I could do something like this right after that:

struct Derived : public BaseEngine {
    bool onLoad() override;
    bool onFrame() override;
};

const std::unique_ptr<BaseEngine> app = std::make_unique<Derived>();

But my idea is, in fact, to not hold the derived class in my header files, and build the library without any possible definition of a derived class, thus, the user can just name it whatever they want in their project.

Of course it won't let me compile it, because I can't construct BaseEngine because it has pure virtual functions.

Then I though of somehow using templates to maybe solve this issue? Now I'm not very familiar with templates, but my idea was to make something like:

std::unique_ptr<BaseEngine> app;
template<class T : public BaseEngine>
void instantiator() {
    app = std::make_unique<T>();
}

Knowing that T holds an implementation for onLoad() and onFrame(). But of course when I need a feature such as templates of explicitely derived classes, no feature exists (not that I know of, at least).

My main question being: is there a way for me to initialize an object from an "unknown" derived class of my known base class?