It took 10+ years to design and build the first SLS rocket, but Artemis 2 is scheduled for May 2024, less than 2 years from now. How much of the second rocket has been built?
The RS-25 engines are re-used Shuttle engines. There are 16 left, enough for Artemis I–IV. So, they only need to start building new engines for Artemis V and beyond.
The booster for Artemis II is completed but not stacked. (The booster segments can be stored almost indefinitely as long as they are separate but once they are stacked, there is a limit to how long the joints maintain their seals.) The casings are (mostly) re-used Shuttle casings, so they don't need to built from scratch and they have enough in stock until the current boosters get replaced by the BOLE boosters on Artemis IX. The segments for Artemis III are already cast and Artemis IV is well underway.
The Orion capsule is essentially finished. However, it uses avionics hardware from Artemis I, so it cannot be fully assembled until Artemis I's Orion returns from its flight and is recovered and disassembled. Work on Orion capsules up to Artemis IV is already in progress.
The European Service Module for Artemis II has already been delivered and work on the ones for Artemis III and Artemis IV is already underway.
The engine on the European Service Module is a re-used Shuttle OMS engine, they should still have enough of those in stock to last well into the double-digit Artemis missions.
The ICPS for Artemis II was already delivered to Florida over a year ago in August 2021.