Can I claim ITC if my supplier has not filed GSTR-1?

Generally no. Under Section 16(2)(aa) of the CGST Act, you can claim input tax credit only if the invoice details have been furnished by your supplier and are reflected in your GSTR-2B. If the supplier has not filed GSTR-1 (or the QRMP invoice facility), the invoice will not appear in your GSTR-2B.

Keep the credit out of your GSTR-3B until it appears in GSTR-2B, and follow up with the supplier to file. You can claim it in a later return once it shows up, within the time limit in Section 16(4). If the amount is large, confirm the treatment with your CA.