Getting rejected for credit cards due to a lack of CIBIL score?

Hi all,
I recently applied for the SBI Cashback and Amazon Pay ICICI credit cards but faced rejection due to no CIBIL score. I have a decent income and primarily need a card for groceries, bill payments, fuel, and online shopping. What are some alternative options I can consider?

@AleenaJacob Consider starting with FD-backed cards like OneCard or IDFC WOW Card. After 6 months, you can apply for unsecured cards.