Build date is on the drivers door jam sticker... also stamped into the block at the front of the motor to the right of the water pump. Sometimes hard or impossible to read, under the paint but it's there. Should show you, in this order... Engine assembly plant, model year, engine size, (340), then probably "P" for premium, then 4 digit engine assembly date in a nice 10,000 day calender format, then the number of the engine on the line that day, mine is also a 4 digit number. If the engine is original and has the partial vin down low on the block on the side this sequence should tell you everything you need... at least it did on my 72 Cuda 340. Good luck. BTW... Nice Challenger!
I added a pic of my 340 while it was out and being redone... the area on the right where the paint was scraped away is where the numbers are stamped. Hopefully yours are there without having to remove the paint. Mine is all re-painted and back now so I can't see them again