Puma in north America number about a million after a time (9)

'puma' is the definition.
('catamount' can be a synonym of 'puma')

'north america number about a million after a time' is the wordplay.
I cannot quite understand how this works, but
'north' could be 'n' ('N' can be a synonym of 'north') and 'n' is located in the answer.
'america' could be 'am' and 'am' is found in the answer.
'number' could be 'c' (C is an example) and 'c' is found in the answer.
'about' could be 'a' (abbreviation in Chambers) and 'a' is found within the answer.
'time' could be 't' and 't' is found within the answer.
The remaining letters 'out' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).

'in' is the link.

Can you help me to learn more?