My first thought is to build a series of objects that when combined represent the finished shape. These you would then progressively move from below the “paper” mesh at the bottom, where they are invisible to the camera, to their final place where they are. To get the effect of the “pen” going around the paper, you could animate the start and end points of a bevel object around a curve?
I have found in the past that the best way to animate something being “made” is to make it completely and keyframe all the positions at the end of your animation, then totally destroy it at frame one and the progressively “remake” it by animating parts of the mesh to appear in their final resting place. I think that to achieve the entire process by progressively adding or making visible thousands of individual parts is possible but time consuming. You can make objects invisible to Blender by either keyframing their visibility property in the Outliner or by using a “hole” type shader (Transparent Shader) and progressively changing it to a visible shader through keyframing the Mix Shader “Fac” variable.
The process in real life is adding very small 3D parts to the blank canvas and you either have to emulate this or animate the gradual appearance of many parts that make up the final mesh. It’s a tough one, but I will give it more thought one the next week or so. But some work with either Materials or moving small pieces may be the answer here. It can be done relatively easy in Houdini (if anything is easy in Houdini), by using particle systems, but I think it is going to be harder/more time consuming in Blender. Maybe someone else has some other ideas…