Cooper’s first to put down the greatest boxer (4)

I believe the answer is:
clay
'down the greatest boxer' is the definition.
'clay' can be an answer for 'down' (thesaurus). I am unsure of the 'the greatest boxer' bit.
'cooper's first to put' is the wordplay.
'cooper's first' becomes 'c' (1st letter of 'cooper').
'to put' becomes 'lay' (as in laying or putting something down).
'c'+'lay'='CLAY'
Can you help me to learn more?
(Other definitions for clay that I've seen before include "Soil used in pottery" , "Material for idol's feet?" , "Brick/pottery material" , "Muhammad Ali's original surname" , "Earth suitable for modelling" .)
