score:3
Things I'm noticing:
Mostly steam ships are depicted. The big one in the foreground also has masts for sails. The first such hybrid ocean liner was the SS Great Western, in service from 1838 to 1856. The last such ocean liner to be built was perhaps the SS La Touraine which was in service from 1890 to the 1920s. The two-mast depiction there looks much more like the La Touraine than the Great Western.
It looks like the central route they drew has a break in it at Panama, perhaps indicating an overland journey there. Overland journeys at Panama were only practical during the days of the Panamanian Railway. That would place it between 1855 (the commercial opening of the railway) and 1914 (opening of the canal).
If we further make the assumption that they'd want to depict the most modern transport possible in their promotional material, It would seem natural to put this towards the earlier part of our window. After 1890 steamships with functional masts might start to look old-fashioned. Thus it looks like the most likely window for this would be sometime between 1855 and 1890.
(Note that later steamships did have vestigal posts where the sails used to go, even if they weren't equpped with actual sails to use on them. They usually didn't seem to have all the extra horizontal rigging I think I'm seeing there. Still, I could be wrong on that score, which would move the end of our window way out to 1914).
Upvote:4
The "Propaganda de Portugal Society" probably refers to the "Touring Club de Portugal", previously known as "Sociedade de Propaganda de Portugal". It's foundation date is 28/02/1906. That's probably why they date the poster as post-1906. The only thing I can guarantee is that it can't be from before, not in that form. Maybe the society recycled some other, older, images from other sources and that's maybe why it looks out of time for 1907 in some details.
The only sources (like this one) I got about the society are in Portuguese (sorry!) but they are quite trusted.