Monetize FB group using print on demand ?

Hello, I've a Facebook group related to a smartphone game.. the group had about 1K game lover in it and 70% of them are active also all the members are from 1 tier countries such as US, UK, some of Germany.. 89% are females. I want a smart way to monetize the group using print on demand (phone cases or shirts I'm not sure yet ) because they're so active and the members are reacting very well with posts and very interested in the game now.
Any advices or ideas you could provide me guys ?

Order t shirt design on Fiverr, submit it on teespring and place an ad on your fb page. Bingo!

I know you asked about pod, but every step you take away from the core product is going to be a harder sale. Can you sell DLC instead or affiliate links to an expansion/related game, etc?

Also, research. What kind of gaming merch is already selling the best to related audiences? Join other gaming groups and see if you find any examples of successful monetization. Search Amazon Merch products. Etc.