Yes you can have a credit score even when you don't have a credit card.
A credit card can help you build credit and raise your credit score if you use the credit card responsibly.
However you can still have credit without use of a credit card.
You can have a credit score by getting loans and paying loans back properly.
If you've never had any credit cards, loans etc then you basically just have no credit history.
You can usually get a credit card or sometimes a loan with a cosigner when you have no credit history.
Then you build up credit and then can easily get approved for credit cards, auto loans, home loans etc when your credit is built up.
If you haven't yet built a credit history, there's no information on which to base that calculation, so there's no score at all.
Once you begin to establish a credit history, you might assume that your credit score will start at 300 (the lowest possible FICO® Score☉ ).
Whats your credit score if you don't have credit?
There's no such thing as a zero score. Having “no score” simply means you don't have any number tied to your credit profile.
You can be absent from the scoring model if you've never had a credit card or loan, or if you haven't used credit in a long time.
Do I have a credit score if I have a debit card?
When you use your debit card, your money is withdrawn directly from your checking account.
But since debit cards are not a form of credit, your debit card activity does not get reported to the credit bureaus, and it will never show up on your credit report or influence your score in any way.