For all our Aura users to track the service status we now report this via our status page: https://status.neo4j.io/
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Yes you can do that so long you purchase Aura direct as unfortunately purchasing from GCP marketplace would prevent you having a free tier instance.
Can you please raise a support ticket https://aura.support.neo4j.com/ so that we can look at this ?
Please detail the versions of your SDN and driver (full stack) and attache the full log for our review.
Pierre - Aura Support engineer