Hello , I believe there is a little bit of confusion in here.
You are mentioning the manufacturing date which is when the batch number is produced and the shelf life which is the number of days to that batch to expire from manufacturing date so I believe you mean the expiry date or best before date.
If you need the manufacturing date , you can revise your batch number policy and use the batch number group with physical date ticked and the date which means your batch number will contain ,within the batch number , when the batch has been generated and ,thus, when looking at on hand on screen you will be able to filter based on manufacturing date.
If you need the expiry date ( or BBD) and it is not available on the ADD field option that is a customisation
Generally speaking , it would be a better idea to create a report of the stock on hand where you calculate for each batch the product life remaning for each batch.
Last but not least , if you are using the advanced warehouse functionality , you can generate picking work based on FIFO or even better FEFO so actually the system picks the stock in the right priority without you assessing any report or stock on hand.