Arceus cannot currently be obtained in Pokémon Brilliant Diamond and Shining Pearl, but it could become available in a future update. Arceus' arrival to BDSP could occur as part of a tie-in with the upcoming Pokémon Legends: Arceus, or a new event could be added to let players capture the Pokémon god. Saving Arceus' inclusion for a special occasion would explain why BDSP does not contain the legendary Pokémon at launch.
Arceus being unobtainable in BDSP mirrors its initial absence from the fourth generation Pokémon games. The Azure Flute from the original Diamond and Pearl allowed players to reach an area called the Hall of Origin and battle Arceus. However, both the event and item were cut from Pokémon Diamond and Pearl's final version and are only restored through hacking. BDSP seems to follow this trend of excluding Arceus, but the games could be leading up to the event's official revival.
Potentially, Pokémon Brilliant Diamond and Shining Pearl could remake the Hall of Origin event as a way of adding Arceus to the game. The event could take place after trainers have defeated the Elite Four, adding to BDSP's post-game content. Given how Sinnoh's champion Cynthia is present in Pokémon HeartGold and SoulSilver's Arceus event, she could be the one to set the event into motion by giving players the Azure Flute. With this, the climactic battle with Arceus from Pokémon Diamond and Pearl's cut event would not only make its first legitimate appearance, but it would do so in the enhanced graphical style of BDSP.
Pokémon Legends: Arceus Could Transfer To BDSP
Alternatively, players might be able to obtain Arceus in Brilliant Diamond and Shining Pearl by transferring it from Pokémon Legends: Arceus. Legends was announced alongside BDSP and is set to release only a few months after the remakes. Legends focuses on Arceus, and it is possible that the Arceus available in Legends might be transferable to BDSP as an official tie-in event. The original Diamond and Pearl utilized a similar approach whereby players could transfer an egg containing the legendary Pokémon Manaphy from the spin-off title Pokémon Ranger: Shadows of Almia. This method could be used again to officially add Arceus to BDSP.
Arceus would not be the only Pokémon added to BDSP through a tie-in. Trainers can obtain Mew and Jirachi in BDSP by having save data from other Pokémon games, gifting Mew for Let's Go, Pikachu and Eevee! and Jirachi for Sword and Shield. Pokémon Brilliant Diamond and Shining Pearl may use this method, or a similarly special event, to include Arceus in an official way.