You can close matchmaking and you will be solo for the story parts of the game (not that long it seems). You can matchmake specific story missions or run them solo, your choice.
The dark zones, which seem to be the biggest areas of the map - feels like maybe 2x or 3x the size of the "story areas" - are PVP zones and you can't avoid other players in them, afaik. Also any items you loot must be "choppered" out, which is a process where you call a chopper in a specific spot and wait for it to come and during that time other players can attack and kill you. Its not automatically a FFA PVP zone, once you shoot an another player a few times you go "rogue" (whatever that means) and anyone and everyone can attack you. It didn't feel like some MMOs though where until you rogue you are not attackable, anyone is attackable anytime I guess just rogue players are highlighted as rogue to warn you.
If you die while you have those lootable drops, other players can steal them. You won't get the items until you attach it to the chopper and it evacs. Once it does successfully get evac'd, the items are yours forever - people can't steal your previously looted stuff, only stuff you have yet to chopper out.
The game also requires an online connection like Destiny, can't play offline.