I hate hair algae! First never vacuum your sand. You can pick up some nassarius snails and they'll sift it for you, gently.
Now for the algae. It's a hard thing to get ride of but doable. I suggest "lights out" this will starve the algae. You can keep them off while your tank cycles. Another thing that causes algae Is if you have your tank near any direct or indirect day light. A good understanding of algae and what makes it grow is helpful, research! Beef up your water changes to 3x weekly, about 20% your
LR is full of nutrients and
detritus, gotta keep it clean! I took my LR out and gave it a good shaking in the old tank water during a water change. You can also harvest the algae as much as you can, with water flow off. Don't want it flying around your tank. Be patient! If it's as bad as you've describe then it may take a little while. I fought it for 4-5 months! Not saying this will be your case but I couldn't go the lights out way as I had corals in my tank.
Hope this helps. Good luck!