I am trying to achieve this effect in Illustrator.
You can use the 'Effect → Distort & Transform → Free Distort' tool and more info here.
Another possiblity is to use 3D effect Extrude & Bevel. It offers easy manipulation of the apparent watching direction. Here the extrusion thickness is zero and the light effects (=shading) are turned OFF.
The adjustment dialog can be reopened in the appearance panel. Click the effect icon there. Expanding the appearance fixes the effect to uneditable.