https://www.nasa.gov/reference/gateway-about/
Gateway Assembly

Gateway launch and staging

The first Gateway elements, PPE and HALO, will launch together to lunar orbit on a SpaceX Falcon Heavy rocket prior to Artemis IV.

Gateway will spend one year transiting to its unique polar orbit, known as near-rectilinear halo orbit (NRHO), around the Moon.

Artemis IV, V, and VI assembly missions
On-orbit assembly of the fully realized Gateway space station will commence with the Artemis IV mission that will launch no earlier than September 2028.

Not going to launch in 2024. May as well resolve?
@JoshuaWilkes

Currently NET November 2024, on a Falcon Heavy. I don't expect problems with the Falcon, but any issues with the payload readiness would push this date to NET 2025.

Northrop Grumman is building the Habitation and Logistics Outpost (HALO) module, and Maxar is building the Power and Propulsion Element (PPE). Northrop will assemble them and prepare them for launch on a single Falcon Heavy. Batteries for HALO come from Japan (JAXA), robotic arm interfaces from Canada, Halo Lunar Communication System (HLCS) from ESA, all going into that single HALO. Northrop has experience building Cygnus but that's a cargo vehicle. Plenty of places for delays to creep in.