It is possible for a java compiler to add an attribute to the CLASS file
format but there is nothing in the specifications to guarantee there is
any information about the compiler used to create the CLASS file.

Maybe you mean what version of the compiler.
In the class file, the first 4 bytes are fixed.
The next 4 bytes give you a number that is related
somehow to the version. e.g. here is the first line
of output from 'od -x' on a file (octal dump in hex format):

0000000000  FECA  BEBA  0000  2E00  2D00  000A  000A  0813

If you flip the bytes, you see 'CAFEBABE' which identifies
the file as a java class file. The next 2 are '0000' then '002E'
The 002E is 46 in decimal and it is the "major" part of the version.
The 0000 is the "minor" part. You need to check this, but
major/minor
45/03 java 1.0.2
46/00 java 1.1
48/00 java ???