It can take a few months to fully stabilize. In my experience larger tanks stabilize faster than smaller tanks. In reality I wouldn't consider any tank truely mature enough that there are no algae blooms for a year or so.
Saltwater is all about patience. Don't do anything too fast, don't over stock, don't over feed, keep nitrate and phosphate (these feed the algae) in check. Don't over react to potential issues. Always ask before reacting. Don't add anything to the water you can't test for. Always quarantine new fish no matter where they come from. Lighting needs to be correct. Coral needs wavelengths more in the blue range and algae needs more in the red range. Having lights meant for reef tanks will help discouraging algae.
It can be frustrating in the beginning but if you stick to it it is a very rewarding hobby.