If it is tiny little green hairs then sure it could be the start of some green hair algae. Since your tank just finished cycling it probably has high nitrates and some phosphates as well. Test your tank for nitrates, nitrites, and ammonia. If your really done cycling as you feed your fish the next few days you will not see any ammonia or nitrites. You will see Nitrates only. If thats the case it's time to change out about 50% of your water for new saltwater and begin weekly changes of about 10%. This alone will help drop your nitrates and give some control over that algae.