Redditor /u/DevilTakoyaki owns a PlayStation 4 and managed to get an early copy of The Surge for their system. While not providing spoilers for the game, they did share some information which might be of interest to other potential players of the game.
The installed game takes up 5.79GB of storage plus another 230MB for Update v1.01. The game has 44 trophies total (1 Plat, 1 Gold, 10 Silver and 32 Bronze).
They also shared a few screenshots and gameplay videos if you are interested in seeing more about the game.