The best way to fight algae blooms is with competition. Algae engage in chemical warfare just like corals. So you want desirable algae to get the upper hand. My algae of choice are coralline algae
First get a good algae control crew. Turbo-snails and hermits worked well for me.
Next, add some pods - tigger pods work well for a fresh tank without competitive species like Amphipods or Mysis. Those guys will also help you keep algae in check and provide food for fish.
Feed lightly and do aggressive water changes to keep nutrient levels low.
Start dosing 2 part calcium & magnesium and add enough coralline seeds like encrusted live rock or scraped off, crushed coralline from another tank (best source is coralline encrusted equipment - a good LFS should be able to give you some) to get them growing.
To promote coralline even further you can also reduce the white component of your light and only leave the blue on.
Lights (completely) off won't solve your problem long term but could rather make it worse as nuisance algae are usually hardier than everything else in the tank. So with making it even harder for their competitors you will actually give the nuisance algae an advantage.
At some point you may also want to set up a little refugium/algae scrubber with chaetomorpha.
