`Date` is a registered field [0] used by origin server as defined in RFC 9110 [1]. Any CDN server will add its own date to that header since it's acting as the origin server for that request.
For Cloudflare in particular, you could try setting Cache-Control to Private=Date and see if the edge cache skips the override [2].
What you want seems to be a tunnel with WAF. In that case, a Cloudflare Worker might be a workaround to the native caching layer but I'm not sure if that has any effect on the edge device updating the Date header or not. Workers do support WAF.
0 - https://www.iana.org/assignments/http-fields/http-fields.xht...
1 - https://www.rfc-editor.org/rfc/rfc9110.html
2 - https://developers.cloudflare.com/cache/concepts/cache-contr...