Thank you, will try that!
Edit: It seems to me that without the platform or physics behaviour, the player will always float through the (solid) ground. The bullet behaviour can only be set to 'bounce off' (otherwise will penetrate solids), whereas the 'set y' action will make the player go through the solid as well.
I am right now having a close look at the tutorial below, which apparently solved the issue I'm having by adding platform behaviour, disabling input and simulated walking. Not sure yet how the simulated walking will work with everything scrolling to the left.
youtube.com/watch