Usually cyber security insurance can be purchased/bundled with other insurance you get from a broker like D&O and general liability. Recommended for anyone doing stuff with analytics or customer data, etc.
You can contact Tammy Nolan from MMA (Tammy.Nolan@marshmma.com) who acts like a broker. You can try Chubb, $3M for $1k/month.
As for AWS, security is on you. Maybe there's a pass through insurance but it would probable only cover a breach directly to AWS and not your employee/user errors, etc.