Digging Down to Reach Stone and Ore?

Quick question, can you dig down to find stone and ore, as in say, from next to a lake instead of into a mountain?

My current town is next to a lake and fairly far from the mountainous region on the map. Currently I’m digging down in an attempt to find stone and ore and I just want to make sure that this tactic isn’t just a waste of time.

Yes, you can see in the border of the map how the layers are positioned. In your case, I think the stone starts after 20(?) blocks.