How do I get sufficient amounts of these resources needed for the buildings? Seems impossible to get these via exploration only.

Look in the item trades for them. Most are usually available for silver or other items. If there aren't any cheap bundles at the moment, feel free to message me and I'll sell a bunch of spare materials. :)

Also some other materials, like vermillion, are much more valuable - for a handful of that you can ask for a lot of silver, or nearly any other item/material. 

100 vermillion sells between 50,000 and 90,000 silver, by the way. Quick money for beginners.

And you might know this already, but the higher your pet's level, the larger and richer their explorable islands become. Between level 41-50 one island can potentially give thousands of silver and dozens of resources. So try to get some higher level pets for exploring.