Difficult question here. If your total time is 2000 hours you will NOT be competitive at the legacy level even with your A330 type. So do you have 2000 hours A330 and a couple of thousand hours more total time? That would change things. Though not necessarily required, but the legacies like to see 1000 hours of jet/turbine PIC time. Even if you get hired by a legacy you will absolutely not fly the A 330, as you’re at the bottom of the seniority list expect 737/320. Because of your low total time you might have to go to a Regional. Not ideal but on the other hand you get part 121 time and can upgrade after have flown 1000 hours in the US. Then you can start building jet 121 pic time. That will increase your chances at a legacy job.
Another option would be to convert your license on your own and apply to the LCC like JetBlue, Spirit, Allegiant or Frontier. Those jobs offer way better QOL and also better pay than the Regionals. That might be an option to wait for a legacy call while building your total time and experience in the US.
I hope I could be of help, feel free to ask more...
Best of luck!