Your credit history from home does not move to the US. You start with no credit file (the record the credit bureaus keep about your loans and cards). That is normal. Here are the real ways to start.
Who keeps your credit file
Three companies, called credit bureaus: Equifax, Experian and TransUnion. Banks report your card payments to them. A credit score (often a FICO score, from 300 to 850) is calculated from that file.
Option 1: a secured credit card
Ask your bank or credit union for a secured card.
You pay a deposit, for example $300. That becomes your limit.
Use it for one small bill, like your phone plan.
Pay the full balance every month.
After a while, many banks return the deposit and turn it into a normal card.
Ask: "Do you report to all three credit bureaus?" If not, it will not build your score.
Option 2: a student or starter card
Some banks offer cards for students or people with no history. They have low limits. Students usually need to show income or money available to them.
Option 3: become an authorized user
A family member or partner with good US credit adds you to their card. Their payment history can appear on your file. Choose someone who always pays on time, because their late payments can hurt you too.
Option 4: use your credit history from home
Some lenders work with companies such as Nova Credit that translate a credit report from certain countries into a US-style report. It works only with certain lenders and certain countries. Ask the card company if they accept "international credit history" before you apply.
You can sometimes build credit with an ITIN (a tax number from the IRS for people who cannot get an SSN). Some banks and credit unions accept an ITIN for cards and loans; call and ask. When you get an SSN later, ask each lender to update your file.
Credit-builder loan: a credit union holds a small loan in savings while you pay it; you get the money at the end.
Rent and phone reporting: some services report rent or phone payments to the bureaus. Check whether there is a fee.
You usually need about 6 months of reported activity before a FICO score appears. A good history takes a year or more.
What builds and what hurts
Builds: paying on time every month, using a small part of your limit, keeping old cards open.
Hurts: a payment 30 or more days late, high balances, many applications in a short time.
Applying for five cards in one week. Each application can lower your score a little.
Paying for "credit repair". You can do everything yourself for free.