Yes, not having a stable job doesn't mean you can't open a bank account.
Key points
The important thing is to choose a product that suits your income level.
The bank may require proof of identity, source of funds, or business activity, depending on the situation and KYC requirements.
If your income is irregular or you're freelance, tell the bank the nature of your work honestly.
Opening an account is one thing, and getting a loan or credit card is another, and each has its own separate credit assessment.