Wooden piece without a screw hole - is this correct?
Considering that the material appears to be particle board, one can presume that the screw is pointy enough to create a hole as it is threaded into the wood. You may get away without a drilled hole but expect to see a disruption of the surface on a scale smaller than the volcano in Hawaii.

If the construction permits, place the wood at the brackets, mark the screw location on the wood. Place the wood on a solid surface and begin to drive the screw into the wood. This will allow you to apply sufficient pressure reducing the chance that the screw will strip out the hole being created.

Once you are satisfied that the screw will progress well enough, remove it and place and fasten into position.

You could use a nail and tap it in the same manner but it might be a bit more difficult to remove it. Maybe tap in stages, wiggle and remove, repeat, then drive the screw.