Uh no need for the CPL conversion.
https://www.ecfr.gov/cgi-bin/retrieveECFR?gp&r=PART&n=14y2.0.1.1.2#se14.2.61_1153
Read 61.153 and use your ICAO ATP.
Everybody wants to go to the Majors including many with more much more experience then you.
Minimum time to be SIC in 121 operations is 1500 hrs.
Join a Regional with a flow through program to a Major like everybody else.
It would behove you to study the applicable FAA publications that are all freely available on the FAA website.
https://www.faa.gov/pilots/training/
When hired they'll expect you to be up to speed with how things are done in the USA as "back home we do it THIS way " gets old real quick
