On 2016-01-21 AWS launched AWS Certificate Manager, which is a free service that allows you to issue a SSL certificate to be used with Elastic Load Balancer and Cloud Front (along with S3 too).
By default, you can deliver your content to viewers over HTTPS by using your CloudFront distribution domain name in your URLs, for example, https://dxxxxx.cloudfront.net/image.jpg.
If you want to deliver your content over HTTPS using your own domain name and your own SSL certificate, you can use one of our Custom SSL certificate support features.
For me I had to upload a simple React website to S3.
As barbolo describes you need a certificate to access site through SSL.
If the static site that you want to deploy is simple enough you can:
Upload to S3.
Do not select "Static Website Hosting"
Convert all relative links (to css, js, etc) to absolute links.