I was playing a game as Castle and couldn't find a sawmill in the first week, which is critical for this race. After carefully studying random maps, I came to the conclusion that the generator places these main mines according to the following principle: the sum of the horizontal and vertical distance between the city and the sawmill/quarry does not exceed 16 cells. This is easy to see if you enable the grid in the map editor. However, the generator places mines in a random direction, not necessarily along roads. In the game, this distance is, on average, 1-1.5 days' travel directly. Another thing is that the mines may actually be separated by terrain, and the path to them may be winding (or even completely blocked by the guards of some other object). But the point is to visually fix in your memory the radius of the circle within which you should search, and not wander around in the far corners of the starting area.
The obstacle tool creates something like "pockets" of terrain on the map, and if the necessary mines are not found in the first explored directions, you should not be lazy and break through to all the "pockets".
On the 2sm4d template, there are potentially 3 secondary starting areas, and each has a sawmill/quarry. That is, if the necessary resource is blocked in the starting area, you can quickly break through to a neighboring area and capture the mine. But again, it will be in close proximity to the city.
On the balance template, this is not possible; wood/stone is only in the starting location.