I might have been wrong about the social channels
After slighly more than twenty days, my follower count on Instagram is above 200 with no ad spend while on Facebook Teapster has less than 50 followers, having spent 20 EUR on advertising.
On the surface, Facebook looked to me like a dead platform (and it's true that I also stopped using it personally a long time ago.)
However, looking at the traffic to the site, I saw a slight bump yesterday and it's actually Facebook that's driving traffic, not Instagram.
This is quite interesting and I will keep monitoring before drawing any conclusions.