I had to go thru the same process with nuisance algae about 1.5 years ago.
I am curious if you are using live rock or dry rock to begin your tank?
About 1.5 years ago, I had flatworm infestation which killed off my tank which included the micro fauna inside the tank as well. As I restocked my corals and fish, my ugly phase hit and I patiently waited for at least 4 or more months. Some of the diatoms/cyano made my coral look unhappy.
At that time I was reading about bacteria diversity by
Aquabiomics using live rocks.
I went and bought 20lbs of live rock and "re-seeded" the bacteria in my tank. I started seeing less and less nuisance algae about 4-6 weeks later. I noticed about about after 3 months sponges growing back on my rock. My corals looked much happier afterwards.
Fast forward to earlier this year in March...I decided to feed my tank Ammonia instead of Nitrate to improve coral growth and colors.... Unfortunately I dosed too much Ammonia and it again killed my fish and corals and affected the micro fauna. Again, I thought I could wait for my ugly phase to go away quickly. It had be 1.5 months and I did not see any quick improvement with 'bacteria in the bottle products' in hopes to have the 'bacteria in the bottles' outcompete the nuisance algae.
I read this thread by Aquabiomics
Effects of live sand & mud on the microbial communities in my tanks (updated with new data)
I purchased live sand and mud and seeded my tank again. It only has been less than 1.5 weeks and I have already noticed a substantial decrease in cyano/diatoms already.
Moving forward, If I ever make another bone headed mistake and disrupt my biodiversity in the tank. I will in all likely-hood use live sand/mud to reseed the bacteria to help accelerate past the ugly phase.