How to sell my new not yet activated Adobe all suite subscription?

There are many restrictions on selling software because, unfortunately, the internet is full of scammers, counterfeiters, pirates and out and out robbers, many of who are stuffing viruses in with their software. Fakes are now very convincing and sometimes run for years before shutting down and leaving the purchaser in hot water. This has really messed things up for legitimate sellers like you: a lot of places won't allow software to be sold at all.

Is the gift just a card with a code on it? If it's just a card, never connected to your Adobe ID or email, it's a thing you can sell. Adobe do not, however, allow selling stuff in their forums.

I don't think you can.  Under the old system, you could transfer your perpetual product license with permission from Adobe first.  But I don't think that extends to Creative Cloud subscriptions.. 

Transfer an Adobe product license

Besides, I'd be very skeptical of buying Creative Cloud from anyone who is not Adobe or an Adobe authorized reseller.