How to create a log file with all SES email sending events

First, explore the options available to you in the documentation: https://docs.aws.amazon.com/ses/latest/dg/monitor-sending-activity.html

When configuring your SES configuration set with CloudWatch as the event destination you need to define the dimensions that you wish to capture as metrics (the documentation has a walk-through of how to do this). This can be more convenient as it allows you to be more intentional of the type of information you find valuable to capture and you don't need to worry about processing the raw data, but it does require more planning.

Since it sounds like you just want the raw event details in CloudWatch Logs, a simple and cost-effective way to accomplish this is to create an SES configuration set event destination to an Amazon SNS topic, and then create a Lambda function with the SNS topic as the trigger. The function code only needs to print/log the event that is passed into the Lambda function. e.g. in Python it would be: print(event). You can have additional subscribers to the SNS topic, so for example you can receive emails of the events if you are still evaluating the ways in which you would like to process the data.

You can also have multiple event destinations for each SES configuration set, so you can evaluate all of the options that are presented in the documentation to determine which best meets your objectives.

Here are links to the pricing details. Depending on your volume and what you choose to configure, you may be able to stay within the free tiers as outlined for each service. Nevertheless, it's best practice to set up a billing alarm so that you are alerted whenever estimated costs begin to exceed your level of tolerance.

https://aws.amazon.com/sns/pricing/

https://aws.amazon.com/cloudwatch/pricing/

https://aws.amazon.com/lambda/pricing/

https://aws.amazon.com/ses/pricing/