Traffic cost about S3

In our AWS account, we have 10TB of S3 egress traffic each month, which is a significant cost. We have considered using CloudFront but found it doesn't fully suit our scenario because each file in our S3 is accessed no more than 10 times. This level of access isn't enough to hit the cache. However, using CloudFront ensures our customers can access resources in S3 with stable loading speeds from anywhere in the world (minimal fluctuations in loading speed). What I want to understand now is: if I integrate our S3 with CloudFront, but in a situation where none of the file accesses hit the cache and all requests go back to the origin, will S3 still charge egress traffic fees?