Open as many as you can. The "penalty" of opening new credits is lower than increasing your limit if you are just starting. Find no annual fee cards that give good welcome bonuses and get some "free" money. If they reject your application you can usually dispute it by calling and asking why and most of the time you can get approved by providing some extra documents. Other than that it's just patience
Source: I migrated 8 years ago and had to start my credit score from scratch
Edit: adding fico score weights
