CloudFront Distributions cannot pass the request to CloudFront Functions before sending to the origin. In other words, they cannot be used to modify origin request/responses. They can only modify the viewer request/responses. [0]

Only Lambda@Edge can help the scenario which I provided, which is also AWS's recommended solution. [1]

[0] https://docs.aws.amazon.com/AmazonCloudFront/latest/Develope...

[1] https://aws.amazon.com/blogs/architecture/serving-content-us...