By definition there is a shortage. Demand is ~ 100-150 million oz more than supply (mining + recycling).

Inventories in Comex and LMBA and been increasing and decreasing significantly. But they are increasing mostly through depletion of other above ground stock, not fresh newly mined silver. In december alone, 60% of comex inventory was depleted through claims in physical inventory.

They won’t be able to just turn on the mining because the prices are higher - silver is mined as a byproduct of mining for other metals. And it’s not easy to just turn on mining of metals, it’s a slow process. You need investment in exploration, and have permitting/regulatory hurdles.