Is it possible or what are the typical actions to apply to prevent being over-billed for AWS usage or any other cloud provider, in case of say, DDoS attack or similar?
One of the example, lets say a public S3 GET access. Yes, it is relatively cheap GET and all other Requests $0.0043 per 10,000 requests, but ,still anyone having an access to the public endpoint, theoretically can generate a traffic and so increase the billing. What is the AWS way to prevent this, if any, or the techniques which could be applied to any cloud provider, and not only AWS.
Specifically regarding S3, there is a good discussion on this topic on another Stack Exchange site here: https://security.stackexchange.com/questions/8583/risks-with-amazon-s3-and-costs
In addition, you could place a CDN with firewall rules like CloudFlare, or Amazon's own CloudFront in front of your S3 bucket in order to improve performance and provide extra DDOS mitigation features.
This is specific to S3, which seems to be your main concern. If you have concerns about other AWS services you might want to create a separate question.