The ZiKZ 5368 becomes available fairly early in the game, but it must be bought from a garage in Russia.
You should proceed to the Taymyr region (on the map screen using
to get to the Global map) and get access to the garage on the first region map, Drowned Lands.
Search for the truck under the "off-Road" category. It costs approximately 31,000 credits.
You can then retain the truck in the Taymyr garage and deploy it back in Michigan and Alaska.
The truck, although it doesn't look like it, has very good offroad capability but lacks diffential lock in the beginning, which must be upgraded later. It can easily pull a fully loaded trailer with cargo, but be careful when driving fast, because of the bumpy behavior on the cabin side.
Save up some missions in Michigan and Alaska so you can use it for deliveries.
If you fear to get it stuck in some areas, think about having a convoy with a strong towing truck. But be sure to switch back to the ZiKZ 5368 when delivering materials.
Achievement will pop after a few runs, depending how you load the truck. (with or without trailer)
In case you‘ve already finished all material delivery missions in said regions, you can also repeat the „Pinewood Express“ timed challenge in the Black River sawmill. After three runs, the goal will be achieved.
Thanks to HomelyBumRocket and Black Dragon RU for the additional input!