W3TC can upload to Amazon S3.
Once you have entered your AWS credentials, all links to media files will be replaced to their location on your S3 bucket, and you will be offered to upload all medias to your S3 bucket which can take a while depending on your files.
During the upload you can pause/resume at any time, or even re-upload all files again.
I did that for the past few years, and have switched to Amazon CloudFront. I’m not using S3 anymore (too slow and too expensive).
I would suggest you to setup Amazon CloudFront instead which works differently than S3:
– It’s a real CDN (S3 is not a CDN) and therefore reported as faster by Google PageSpeed Insight
– It’s less expensive than S3 as you don’t pay for storage but only for bandwidth
– You don’t need to upload your files, Amazon CloudFront will request the files by itself from your server upon user requests. That means that only files actually in use will be stored on the Amazon CloudFront CDN.
When using Amazon CloudFront you don’t need to use S3, simply specify your existing web hosting as origin (Amazon CloudFront will download files from your hosting only once).