AWS EC2 - Use IAM role to serve static website hosted on S3

I am hosting a simple static website on a Amazon S3 bucket and my problematic is : I need to serve this website via an EC2 instance.

All documents in my S3 are not publicly accessible.

I have set up a role which can list my buckets and which have all authorizations on it, and on my EC2, I am able to see my bucket and list/update all the files that are in the bucket.

I have set up an NGINX reverse proxy on my EC2 instance (which runs with the previous IAM role) which redirect requests to this server to my S3 bucket. However, I am getting a 403 error (Unauthorized).

Here is my nginx configuration file :

server {
        listen 80 default_server;
        location / {

                proxy_http_version     1.1;
                proxy_set_header       Authorization '';
                proxy_set_header       Host my-bucket.s3-website.eu-west-3.amazonaws.com;
                proxy_hide_header      x-amz-id-2;
                proxy_hide_header      x-amz-request-id;
                proxy_hide_header      x-amz-meta-server-side-encryption;
                proxy_hide_header      x-amz-server-side-encryption;
                proxy_hide_header      Set-Cookie;
                proxy_ignore_headers   Set-Cookie;
                proxy_intercept_errors on;                                                                                                                                                                   
                add_header             Cache-Control max-age=31536000;
                proxy_pass             http://my-bucket.s3-website.eu-west-3.amazonaws.com/;
        }
}

I guess that my proxy does not use my EC2 IAM role to make the request.

How can I achieve this (make a request to my S3 using my IAM role) ? Do I have to set up a S3 policy so that my reverse proxy works ?

Thank you for your answers !