I have this object with a material I created with an image, how can I manage to add thickness to it ? I already tried adding the solidify modifier but could not get any result...

Here is a screenshot from Blender, as you can see the object is totally flat. How can I give it some thickness ?
Thanks,
Edit: Here are screenshots with "Only Rim" checked and not checked to give a better idea of what I get but is not good

