So it's a bacterial bloom.
Do you have any live plants in the tank that may be looking a bit iffy? decaying plants are organic matter too.
Brown algae (actually diatoms) are common in new tanks as they thrive on ammonia. There's plenty of ammonia in the water with both fishless and fish-in cycling. The brown usually goes away by itself as the tank matures.
As for the bloom, it is basically harmless to fish, just unsightly; though it can make it tricky to see the fish and you do need to keep an eye on them when first bought. The bacteria do compete with fish for oxygen, so if you get fish make sure the filter outflow is rippling the water surface to enable maximum gas exchange. The bloom bacteria grow floating free in the water and they multiply so fast we can see them as the cloudiness. Because of this fast multiplication anything we try to get rid of the cloudiness doesn't work - they grow too fast for us to keep up with. Once the bacteria have used all their food supply they will die, but it is impossible to say how long that will take as every tank is different.
It is up to you whether you want to get fish while the bloom is still there. If you would prefer to wait, add 1 ppm ammonia every couple of days till you are ready to get fish.