S3 bucket behind VPC needing custom SSL cert

The short answer is no. First because S3 static websites feature do not support SSL. This is a total different feature than using S3 as a regular object storage, in which you do not use HTTP protocol to GET HTML web pages or other static content, you use API calls to S3 API which are different endpoints (and they are TLS with s3.amazon certificate). So, when you deploy a VPC Endpoint (it doesn't matter Network or Gateway) you are accessing the S3 API not the feature which supports WebSite hosting which has a totally different endpoint and cannot be accessed using VPC Endpoints for this reason. So, if you want to access your website form a private IP you cannot use VPC Endpoints. If you want to expose a public website with a custom SSL certificate, the best approach is to use CloudFront (pay per use and you remove proxy management).

I hope to have helped you to clarify your question.

Best,