What year was my MacBook Pro made?

For most models, the information @BobTheFisherman mentions will be close enough since many models are discontinued in a year or so. The biggest exception is the MBPro 13" (mid-2012) non-Retina model which was released in 2012 and was not discontinued until 2016.

It used to be possible to calculate the manufacturing date down to a one week period, but Apple recently changed their serial numbers to be random so AFAIK, there is no way to determine a manufacturing date on more recent models. Even the ones sold between 2012 - 2020 (or there abouts) had a more complex method of calculating the manufacturing date. With the 2012 & earlier models, the manufacturing year and week number was found with third character being the year, and the fourth+fifth character being the week.

You can use the information from the following website which lists the dates when a particular Mac model was being sold:

https://everymac.com/

Edit: The MacTracker app for macOS also is a good source of this information...it has information for every Apple product and OS since the beginning.

https://mactracker.ca/

Click on the Apple icon located in the top menu left side. Click on About This Mac Overview to see the model/year of the Mac. Sorry but his is not necessarily the year manufactured.