Optional constructor injection arguments with .NET Core

In your example, you provide the serviceProvider with a runtime value currentDependency. Application components should not require runtime data during construction, as explained here. The solution is to refactor your design, as explained in that article.

About optional arguments:

The fact that some DI Containers support optional arguments, doesn't make it a good practice to use them. As a matter of fact, injection constructor arguments should never be optional.

As explained in this article:

An optional dependency implies that the reference to the dependency will be null when it’s not supplied. Null references complicate code because they require specific logic for the null-case. Instead of passing in a null reference, the caller could insert an implementation with no behavior, i.e. an implementation of the Null Object Pattern.

If not, what is a clean solution for this sort of problem?

As stated, the Null Object pattern is the solution for this, even when using a DI Container that actually supports optional constructor dependencies.

Normally, I create a factory by hand in this case.

public class TheFactory
{
    public TheFactory( SomeType fromContainer )
    {
        _fromContainer = fromContainer;
    }

    public IProduct Create( SomeOtherType notFromContainer ) => new TheProduct( _fromContainer, notFromContainer );

    private readonly SomeType _fromContainer;

    private class TheProduct : IProduct
    {
        // ...
    }
}

If you need per-product dependencies from the container, the factory's Create has to resolve them. Or, in the case of e.g. unity, the factory gets a Func from the container.