Hard to say without seeing it, but my first thought is 1/4 inch hardwood plywood. The thin sheets are pliable. So you install one sheet and then using good glue, laminate a second sheet on top of that one. This assumes you have some structure behind the sheets that you can drive screws into. You can add more sheets to get the desired thickness but probably two would be enough. Once the glue sets you can remove the top layer's screws and use wood putty to fill the screw holes.
The problem with this is that you would never be able to remove this in the future.
There may be better solutions.
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