Early game it is not uncommon to have to make a kiln and use it for a while then tear it down and make a smelter to use for a while. After just a short time, though, you should have more of these than you ever need, I have > 50 in a chest.
Note that these have a number of uses beyond the kiln & smelter. Keep all you find until you have a good supply put away.

Without being too spoilery here: in the swamps, a special mob will randomly drop them when they die. So you can go to that same spot and farm the mobs to get them, and there are clever ways to kill them instantly. You can figure it out.
For me it is just easier to roam the black forest and when I'm attacked by skeletons I know a burial grounds is near. Just raid that to get the few surtling cores you need. As you gear up and level up your blunt weapons, skellies are easy to kill and take their surtling cores.

No, but there are other sources of them, and typically a world has LOADS of them.

Range ahead, search and explore, raid neighboring islands for resources like a Viking!

Originally posted by Soulstinger:

No, but there are other sources of them, and typically a world has LOADS of them.

Range ahead, search and explore, raid neighboring islands for resources like a Viking!

Dang! I'm literally one off from making a smelter haha