Is it possible to confirm CD was burned on a particular machine?

"I believe it depends on the manufacturer. Here's an article from the EFF that details the digital fingerprints left by CD burners.

Most computer users are unaware that CD burners in their PCs also
contain a similar tracking mechanism that embeds a unique serial
number, called a Recorder Identification Code, on every CD they burn.
(As far as we know, this mechanism has also been extended to DVD
burners.) This rule is enforced by Philips via its patents on the CD formats. The standards for the RID code are not directly available to the public, but Philips writes:

As result of the discussion in March of 1995, between the consumer electronics manufacturers and the recording industry [...] it will be possible to trace each disc back to the exact machine on which it was made using coded information in the recording itself. [...] The RID coding system, which has been incorporated in the various Orange Books which contain the CD-R and CD-RW Standard Specifications, specifies a system which enables every CD recorder/rewriter to write its unique ID to every CD disc recorded by that CD recorder. [...] THE USE OF THE RID CODE IS MANDATORY."