Based on one of the greatest video game series of all time, Fallout is the story of haves and have-nots in a world in which there’s almost nothing left to have. 200 years after the apocalypse, the gentle denizens of luxury fallout shelters are forced to return to the irradiated hellscape their ancestors left behind — and are shocked to discover an incredibly complex, gleefully weird and highly violent universe waiting for them. From executive producers Jonathan Nolan and Lisa Joy, the creators of Westworld, starring Ella Purnell, Aaron Moten, Walton Goggins and more. All episodes arrive April 11 on Prime Video.
She is wearing a vault 33 suit. Since it isn’t a vault from any of the games we don’t know when this is. It could be before Vault 13 opened up in the original game, then the vaultdweller will not have helped Tandy in Shady Sands join together with other towns to create the NCR yet. The Brotherhood having the large airship seems out of timeline though they might have had it all along and just not brought it into the open until Fallout 4.
In the Vanity Fair article. Says the show takes place 9 years after the events of Fallout 4, in 2296. The first game is set in the year of 2161.
Archive link of the Vanity Fair article