Usually, as in this case, when you see a date printed on a piece like that it is not the date the piece was made (most of the time). It could be the date of the stein style or artwork on it that they modeled it after. Oftentimes when there is a printed date on a piece it stands for the date that the company originated, but 1600s seems a bit early for a company to have been established in when this piece is, I would guess circa 1950s. There are other people on this board that know more about West Germany pottery than I do, but keep in mind West Germany was called such from 1949-1990. If you can get a better up-close picture of any markings it may help, but this would be difficult to identify a maker if all that's on there is "Made in West Germany" and the number "2" which is what it looks like to me from your pictures. Unfortunately steins don't typically sell for much even if they have lids. (What people are asking for them online and what they sell for are two totally different things.) All in all if I were you I'd keep it, it's a cute decorative piece.
When I say they don't go for much--not to discourage you, but I had a gorgeous midcentury colorful hand painted, very decorative stein with a hinged metal lid that recently sold for $5.50 on eBay. A contact of mine in the antiques business advised me to stay away from trying to buy & sell steins because the majority of them sell for very cheap. I think he was right! But hey, you got a great mug out of it!
