Selling the illusion
In the Hammer editor, the time machine is nothing but a teleporter that takes the player to a different room, that looks the same as the first one layout-wise, but is overgrown and looks older aesthetically.
In the game, the illusion of time travel is sold to the player using some camera shake, some fade-in and fade-out effects, but also through the placement of the teleporters. When you teleport through time, the player position and rotation remains the same but the portal changes position. This makes the transition between time and space seemless and smooth.
Just in case the player didn't understand that the two rooms were one and the same, but set during different times, I also shaped the rooms in a unique and recognizable way as well as place a poster in the same spot in both rooms which read "REMEMBER! If a future you tries to warn you about this test, DON'T LISTEN".