How/When did the US Government make its warships from wood to metal.
The US government just invested in the best technology available at the time. Manufacturing in the early 1800s increased a lot. We got higher quality steel, at industrial scales and precision machinery. The same technology that goes into making a steam engine is the technology needed to make guns and ships hulls. So guns became bigger and shells more advanced, exploding on impact. In 1853 the Russian Navy sunk the entire Ottoman Navy in 30 minutes without suffering a single loss because they had more modern guns. It became obvious that wooden hulled ships were obsolete. The French and British hastelly built some iron warships to meet this Russian fleet. And later on in 1857 the French were already building large ocean going iron ships. The British followed suit shorty after.
The US were a bit late to this new technology but were able to get experienced from the Europeans. Old trees for building strong ship sides were plentifull in America and the industrial metalworks were not as many or as advanced as the European. But when the civil war broke out both sides were rushing to make iron battleships like the Europeans had.
US Civil War or thereabouts.
Armoured ironclad ships, ie partially metal ships, were fairly impervious to shipboard cannons from the time. The first fight between two of them, on March 9th, 1862, took some three hours and eventually both ships withdrew with no significant damage. Why? Again, because the metal armour on the ironclads made them all but impossible to damage with the cannons of the time. This fight meant the end of fully wooden ships as ironclads had shown to be vastly superior in just a single battle.