Personally, I wouldn't wait, because credit can take a long time to build (just getting an unsecured card will take a year).
You may also be able to get a card from a bank in your country of origin, some have branches or affiliates in the US.
So when I immigrated to the US, I started with a secured credit card as fast as possible. Mine was free to have, and you could set it up so it was paid automatically, in full, from your checking account every month. That way you just need to charge something to it each month, and you'll slowly build your history.
You don't even have to do that. You can leave it idle for months if you want. The only thing you have to watch out for is the issuer canceling inactive cards. Having an idle credit card shows you aren't maxing out your cards - you have credit available that you are not using. Length of credit history is also a factor in your score.