Hi Deepak,
I'm afraid you're stuck. Omega will give info about vintage watches, this costs 50 CHF. But they don't provide Info on non-Vintage watches.
I think this is to protect their dealers who may have had a watch in the stockroom for quite a while. Imagine if Omega provided this Info, some customers would then go back to the dealer & ask for a newer model. ( There are plenty of people like that ).
I'm not sure if your watch is a chronometer or not, but if it is, there is a "trick" you can use.
Omega will provide, for free, the Chronometer certificate for any of their watches, that are under 5 years old & have been bought from an AD.
If this covers your watch, you need to write an E-mail to aftersales@omega.ch send them various scans of your warranty card ( showing model number, serial number, purchase date etc etc )
The will send you the Chronometer certificate. this IS dated. Now, whilst this ISN'T the manfacturing date, or the date the watch was shipped to a dealer, it's a rough estimate. You'll be able to see when the movement was tested. The watch was assembled & shipped AFTER this date.
I hope this helps & let us know how you get on.
Steve