Silver will only spawn in the tallest mountains. It is possible to have low mountain biomes which will have no silver. In that case, you need to move on.

Stone Golems are only weak to pickaxes. You can find a way to get on top of their head and mine them, but staying on top is tricky. Otherwise, you can whittle them down with arrows (slow) or work up the nerve to parry their attacks and hit them while stunned (risky).

You will need to collect at least one of each ingredient and have a sufficiently leveled workbench to unlock those recipes. Make sure you've collected guck from the swamp, if you haven't already. Once you've smelted silver, everything else should already be in place.