First place I always look is on the base of the rear view mirror. Pull the mirror off its mount ( it is attached by a strong spring, which is a safety feature ) and see if you can spot any numbers printed on the mount base. These numbers can be deciphered fairly easily.
Other good places are the wiring loom section labels. These are a bit harder to get at, but usually have the date of manufacture printed on the white vinyl part-number labels that are woven into the loom insulation. Eash section of the loom has a label.
If you have an original Factory steering wheel, you can often see the manufacturing quality control 'Ken' stamp on the alloy centre casting or on the brass part of the horn ring mechanism. Again, it is possible to decipher the date stamp. There are other places all over the cars.
Bear in mind that these are component manufacturing dates, and they need to be cross-referenced with others on the car to form a more complete picture.
Once production was in full swing, parts were being manufactured, delivered to Nissan Shatai at Hiratsuka and attached to production vehicles within a matter of just a few weeks. On average ( don't take this as gospel, as we have to be pragmatic ) you will tend to see something between three to six weeks between component manufacture and a complete car coming off the production line. Sometimes more - but usually around that kind of time frame it seems.
Look out for the Japanese year dating system though. You will often see the numbers for the 'year' section of the date use the national system relating to the year of ascendancy to the throne of the incumbent Emperor. First-generation ( S30-series ) Z cars were all built during the reign of Emperor 'Showa' ( known outside Japan as 'Hirohito' ). He ascended the throne in 1925 - so 1925 is 'Showa 1', and 1969 was 'Showa 44'. Hence you will see 'Ken-sa' stamp dates such as '71145' for example ( meaning 7th November 1970 ) - but not all component manufacturers ( and there were many component manufacturers on these cars ) used the same dating system - so keep an open mind.
Let us know what you find.