There is no specific timeline for algaes to start appearing. It really depends on the amount of nutrient and water source used for the most part. It's actually a good sign.
Once you get the water tested post the results.
FWIW, I think you would be much better off purchasing the basic test kits so you have them on hand. When problems arise you will often not have the time to wait.
NH3,
NO2,
NO3 and pH being the minimum.
I would also suggest increasing the temp a bit more. 76° is a tad too low. Shoot for 78-80° which is a fairly decent "happy medium".
What's the salinity?
As far as the lights go, they do contribute to the growth of algaes but it won't make any diffeerence if you run the now or later. The algae will still be there waiting for the right conditions to grow.
IME, it's best to just let it burn itself out, especially in a newly cycling tank.
Cheers
Steve