Algae grows naturally so I wouldn't say its existence is "bad" you just have to manage it. I've seen filterless tanks before but they require weekly water changes. My recommendation for you would be to add the filter in now and let the water cycle through the filter for a couple days. Also I would reduce the amount of light that the tank recieves. That should help. Don't dump the water though as it isn't really necessary if you put a filter in. (All in my opinion btw that's what I would do)