How to create an instance of generic type whose constructor requires a delegate function parameter?

I need to use the following generic class and method ParseFrom() in it:

public sealed class MessageParser<T> : MessageParser where T : IMessage<T>
{
    public MessageParser(Func<T> factory); //constructor
    public T ParseFrom(byte[] data);
}

Now, I do not know the type of the parameter for this class at compile time, so I use type reflection and MakeGenericType() method to do that:

//Assuming itemInstance is given as input parameter 
Type typeArgument = itemInstance.GetType();
Type genericClass = typeof(MessageParser<>);
var genericType = genericClass.MakeGenericType(typeArgument);
var instance = Activator.CreateInstance(genericType);

It gives me a runtime error: MessageParser<> does not have a parameterless constructor. But when I try to pass Func<T> factory as a parameter for CreateInstance():

var instance = Activator.CreateInstance(genericType, () => Activator.CreateInstance(typeArgument));

it gives me a compile error: Cannot convert lambda expression to type 'string' because it is not a delegate type. Am I using the wrong syntax for a delegate function here?