Can I apply for a credit card when I just started working 3 months ago with no CPF contribution? I just graduated and earning $3.6k a month and have been working PT since Dec 2020.

If you can produce your income pay slips or account statement. The bank should be able to approve your application.

But typically the requirements might be higher or more stringent. Worst case scenario your credit limit is pegged to the average of your monthly income

Will be difficult, for jobs with no CPF contribution, need to submit Latest 1 or 2 year of Income Tax Notice Assessment (depends on bank), which means need to work for a year then file income tax.