Not for the faint hearted, but within the capabilities of most DIY types.
DO NOT poke and prod at the hole /dent. Just cover it with sellotape.
Remove the table top from its supporting frame.
“transpose ” the location of the “damage to the bottom of the table .
Most damage is only rarely any bigger than an inch / or 10p coin. Thus , drill a similar size ” access hole” in the underside of the table
Just deep enough to get through the ” ply wood ” under side, to reveal the ” egg box packing / support , being careful not to dislodge the underside of the damaged area on the table surface .
Once exposed , lay the table face down on a thin towel on a very firm surface. The traditional kitchen table comes to mind.
With gentle pressure push the damaged area back in to place. ie.,push them firmly with a flat surface. Potentially a screwdriver handle or the flat end of the handle of a bolster or similar.
Check the :” damaged area” has been reshaped to a satisfactory standard .
Cut / prepare a thin piece of formica or ply wood to make a plug small enough to fit through the “access hole” , but large enough to overlay the underside of the damage area.
Apply suitable wood adhesive to the plug and place it glue side down against the damaged area, and repeat the firm pressure on the plug against the underside of the damage. Even a gentle tap with a hammer may help.
Hence the need for the flat surface and a firm platform to perform the operation .
If you can , maintain pressure on the plug , wait until the glue dries .
Once dry , cut and prepare a plug to cover the access hole on the underside of the table . Apply with suitable glue and when dry , fully inspect the damaged area. Most of the surface will be sound, but any obvious damage can be disguised with matching emulsion paint , or risk some very fine filler prior to the paint.
When it s all dry , refit the table and remember to remove what fell out to a different locker and place a suitable table cover on the table,