Large image in smaller composition

You just change the Composition width and height as you would for any Composition.

That is, select the 4000-by-3000 Composition that resulted from importing the layered Photoshop file as a Composition and then choose Composition > Composition Settings.  In the Composition Settings dialog box, change the width and height to 1920-by-1080 and then click OK.

I'd like to suggest a different approach:

In the 4000-by-3000 Composition that resulted from importing the layered Photoshop file as a Comp, create a new Solid (Layer > New Solid) that's 1920-by-1080 with the Fill color set to 50% gray (it can be any color).  Add a Mask by choosing Layer > Mask > New Mask while the Solid Layer is still selected in the Timeline.  Add a Stroke by choosing Effect > Generate > Stroke while the Solid Layer is still selected in the Timeline.  In the Effect Controls, set the Stroke Color to red, the Brush Size to a value that's easy to see (it defaults to 2.0, but you may want to increase it to 10.0 to make it easy to see when the Comp magnification is set to 50% or smaller), and most importantly the Paint Style to "On Transparent".  Lock this layer and keep it as the front most layer (that is, layer number 1) as you animate.

This approach allows you to see your layers outside of the 1920-by-1080 area.

When you're ready to render your animation, nest this 4000-by-3000 Composition into a 1920-by-1080 containing Composition for rendering.

If you'd like to see just the layers inside the 1920-by-1080 area of the 4000-by-3000 Comp as you work, double-check that the Solid is the front most layer, hide the Stroke Effect and change the Layer Blending Mode from Normal to Stencil Alpha.  If you locked the layer earlier, you'll need to unlock it to make these changes.