You sure that's not a bacteria bloom instead? I just started cycling a 50g a handful of days ago, and the first day or so, it was cloudy from the sand, but the last 2-3 days it's been hazy due to the bacteria from the sand + bottle (Dr. Tims / MB7).
In my experience, bacteria blooms from an initial cycle cleared up within 3 days or so after the bloom started.
Honestly, I think you should just get a hob filter with some filter floss/pad and just wait it out- since you'll kinda need one anyway, right? I don't think I saw a filter on your tank. I guess you don't really need one, but you know.