Is it possible to create a Dynamic Module without using the Back End Module Builder tool?
Sure, it's possible, but it's a very time-consuming task. I wouldn't recommended it unless absolutely necessary. The documentation explains how to do it.
I was hoping it's possible to do it programmatically. The following code will not work but demonstrates what I am trying to do.
//Create the module.
//Set the properties of the module.
b.Title = "Testimonials";
b.Description = "Customer Testimonials";
b.ContentTypeName = "Testimonial";
//Save the changes.