I have no idea how I've apparently upset you so much with my reply, but I'm sorry
I believe your point is that new sand will experience an ugly phase and that's true. I believe you are also taking the OP's word that they have Cyano, but we don't actually know that for sure because we've not seen pictures, and as I've mentioned, the very low nitrate and phosphate is thought by many R2R members to be a cause of Dino outbreaks. I believe it's more than possible that the OP has dinos with or without some cyano. Dinos are harder to deal with than Cyano, and I would address this first.
I am also sure you've seen charts or advise calling very low or even zero nitrate and phosphate. I promise that this is old information, and not what the majority of reefers aim for these days.
Further, I've linked to an article from Randy Holmes-Farley above. If you're unaware, RHF is a PhD Chemist and a well know reef tank guru for probably 30 years now, and across multiple forums and publications. In the article I linked, Randy shares his advice for target nutrients, and the reasons why, and many of us here at R2R are now following his advice, which is to let nitrate float between 5 ppm and 50 ppm, and phosphate from 0.06 ppm to 0.30 ppm. This is for coral health primarily and to minimize the chance of dinoflagellate algae.
I hope this helps!