I have the artboard's dimensions set to 1000px by 1000px. I am trying to create a circle that fits perfectly inside the artboard without the circle's edges being "cropped" out, which happens when I set the width of the circle to 1000 px and the height to 1000 px. (like in the picture). Also, the circle is placed in the middle of the artboard.
By default, strokes will align to center, which means half of the stroke's weight will slip outside the artboard for objects touching the edge of the artboard. This is made visible in the image below where each circle is the same size and same stroke weight, but with differently aligned strokes.
Assuming you have both the artboard and circle already set up at 1000x1000 pixels and the circle is centered inside the artboard, all you need to do is set the stroke on the shape to align to inside. This will push the 'line' to the inside of the circle so the object fits completely inside the artboard.
The same thing explained in the official docs.