The cycle will proceed fine whether or not the water is a bit cloudy, as MW said. The bacteria you are trying to culture in a fishless cycle live on surfaces with a good flow of oxygenated water. The largest such surfaces in an average tank are in the filter. The cloudy water lasting a day or two is not unusual for a sandy bottom. When I set up my 55 gallon with sand, it took almost 4 days to look clear and that was in summer when I was able to very thoroughly wash the sand. There should not be a need to clean the filter for several weeks in a new cycling tank. Until the filter starts to show decreased flow, the filter is fine.
Looking at your setup, I see that the tank is in a spot likely to get a fair amount of light. That could end up causing algae control problems if you don't have enough fast growing plants to remove all of the plant nutrients from the water. With high light, algae is a tough thing to control sometimes. There are also schools of thought that advocate some direct sunlight, like the El Natural method of working with plants. In that system you would be using potting soil under a layer of sand or gravel rather than using straight sand as a substrate. It is generally not a plant beginner's best bet but I have a tank running that way with some success and I am no expert on plants.