Yes, it is a statics question: you don't have to consider acceleration or velocity.
To lift the roller onto the tiles you only need enough force to match (plus the teeniest bit) the maximum opposing force. In general, that entails calculating the opposing force at each stage in lifting the roller onto the tiles, but I think it's pretty clear the maximum opposing force will be right at the start. So all you need to determine is the push/pull needed to make a certain force become zero... which one?