The key to this room is to KICK the box not push it. If you push it you'll never make it.
Pull the box out of the gated room so that you have just enough room to push it and then kick it at full strength (R1+X and don't release until Kratos stops grunting - then release X).
Kick #1 - to the corridor
Kick #2 - to the end of the turn
Kick #3 - to the bottom of the ledge
Keep in mind, you don't need to kick the box to the very end - just enough so that you can climb on top and double jump to the ledge.
You'll make it just in time!
I managed to complete this area by pulling the box the entire way... I never kicked it even once.,
My trick was the minimize the distance and cut all the corners. I pulled the box from the closet, dragged it diagonally to the hallway, and then kept the box against the wall closet to the ledge as I dragged it up the hallway. When I started approaching the final room I pushed slightly towards the wall so that as soon as the box cleared the wall it would start sliding towards the ledge. Once the box was under the ledge just enough to provide me with something to grab on to I jumped up and onto the box and pulled myself up. The box was destroyed by the time I got on to my feet.