Instead of scrolling the tilemap, you could just have your character and camera constantly moving in the direction you want them to travel, as well as recording your player movements. Instead of having the camera focused on the player, have it focused on a separate Node2D, which will be the middle of your screen. You can also have a moving collision box around the camera to prevent the player from leaving the game screen.
The reason to do it this way, rather than by scrolling the tilemap, is that you'd also have to scroll every single other "non-moving" object in the game. It's much easier to just move the camera and player simultaneously.