Amazon Route53 hides most of the contact information by default, however that doesn't include the Creation Date property. Is there an option to hide that piece of information as well? I do not want the public to know when I created my website.
Unfortunately, you did not mention the top level domain (TLD) you're referring to. In case of e.g. .com (or another gTLD), you can not avoid having the creation date in WHOIS. See Appendix F of the Temporary Specification for gTLD Registration Data, being effective as of 25 May 2018, for more details.