The HTTP protocol has the Date
header (RFC 7231, 7.1.1.2) for the date and time at which the message was originated. That's typically the time on the server in UTC.
When a Date header field is generated, the sender SHOULD generate its
field value as the best available approximation of the date and time
of message generation. In theory, the date ought to represent the
moment just before the payload is generated. In practice, the date
can be generated at any time during message origination.
This is not really fingerprinting nor hacking, but a feature of the protocol. Also, every reasonably configured server should be configured to automatically update and keep correct time using NTP. The information you are looking for could only be somewhat useful if it wasn't, and in very specific conditions as discussed e.g. in Is exposing the server time a security risk?