Finally I also moved my homepage to a static one. First started ambitious with Gatsby but a bit shocked that it seems that I have to redesign my template, I went with the most simple way:

• copied WordPress site to local -> https://localwp.com/
• installed the plugin Simply Static by Patrick Posner
• exported the site to static files (relative URL)
• uploaded to AWS S3
• added AWS CloudFront for ssl / https
• added a CloudFront function for new URL schema (with the static pages it’s subdirectory/index.html instead of subdirectory/), Example: https://docs.aws.amazon.com/AmazonCloudFront/latest/DeveloperGuide/example-function-add-index.html

And finished with some minor bugs but hopefully a better experience for everybody – including preserving the old URLs for web search.