Can I dive in Silfra without certifications?

No, you cannot go diving in Silfra without certifications.

All divers must have at minimum Oper Water diving certification from an internationally recognized diving organization as well as a Dry suit diving certification OR 10 logged dry suit dives within two years of the Silfra tour date. These 10 dives must be confirmed with written proof signed by a diving instructor. The rules are set and upheld by Thingvellir National Park.

The good news is that you can Snorkel in Silfra without any certifications.