Push one's way through American street (6)
I believe the answer is:
thrust
'push one's way' is the definition.
'thrust' can be an answer for 'push' (thrusting is a kind of pushing). I am not sure about the 'one's way' bit.
'through american street' is the wordplay.
'through american' becomes 'thru' (US informal spelling of 'through').
'street' becomes 'st' (abbreviation).
'thru'+'st'='THRUST'
Can you help me to learn more?
(Other definitions for thrust that I've seen before include "press" , "Push forward with truths" , "Sudden push" , "The essence" , "Violently push -- gist" .)