Hi Cam,
Can't give you a build date, but you can get to the year...
Lister used 3 serial numbering schemes for the CS (and other engines): Plain numbers (usually prefixed "CS") until 1951, a "coded" system from 1952-1970something, then a different coded system.
Yours looks like the middle system, and therefore breaks down as follows:
676 3/1 3
This means it's the 676th 3/1 type engine built in 1953 (the last digit or 2 digits, one adds 1950 to get the build year).
HTH!