Can we extrude an imported SVG?

I’ve imported an SVG file I created in Illustrator CC. It is a simple heart shape.

I’m having trouble extruding it to give it a thickness. If I Add > Mesh > Plane, I can E, 1 and get an extrusion, but the combination doesn’t work with an imported SVG file.

How do I extrude an SVG file? Can it be done?

Here’s an answer that worked for me: