CloudFront for website with custom CMS hosted out of AWS

I've got a website with custom CMS hosted outside of AWS.

How can I set up CloudFront? My idea is to upload current content to S3 bucket. Set CloudFront up with origin from that S3.

This also require some changes in CMS itself:

• To replace static content (pics) urls for the one from S3bucket.
• Check if file exists on S3 then use S3 if not use copy on local server.
• To interact with S3 butcket API. (uploading/deleting)
  • When uploading new file, upload it to S3bucket too
  • When deleting file, delete it from S3 too
  • Delete only from the bucket.

Is there any other easier way? Mayby I'm just overthinking and cannot see the simplest solution.