Just start refilling and chlorinating.

If you are confident you can go lower than 6", do so. Under the circumstances, dichlor would be a good choice:


For start-up of a freshly filled pool, or a pool that has lost its stabilizer, dichlor is ideal for many folks since it adds BOTH chlorine and stabilizer, and is quick to dissolve. There are a couple of cautions: don't dump piles of it on the bottom of a vinyl, painted, or fiberglass pool; don't add large amounts at one time to pools that have copper or any other metal present.

The other difficult is with purchasing it. Most retail sources have embraced the concept of selling diluted dichlor for an undiluted price. Not only does this cost you more, but some of the dilutants actually hurt your pool! Sams Club is the only retail source that is consistently carrying undiluted dichlor. Walmart and Kmart seem to carry ONLY diluted stuff. Home Depot and Lowes vary from region to region, but you must be an 'expert label reader' to buy from them. If you do check labels, avoid the Pool Time and Aqua Chem brands. These BioLab brands seem to have pioneered the concept of diluted chlorine, and are very, very good at it (= tricky!).

PoolBrand granular dichlor 50lbs @ Sams Club => ~$2.20/lb (May 2014 in Chattanooga)
PoolBrand dichlor bagged shock 24lbs @ Sams Club => ~$2.50/lb (May 2014 in Chattanooga)

Kem-Tek dichlor 22 lbs @ Amazon => ~$3.50/lb (May 2014)
Kem-Tek dichlor 12 lbs @ Amazon => ~$4.10/lb (May 2014)
Kem-Tek dichlor 5 lbs @ Amazon => ~$5.00/lb (May 2014)
Kem-Tek dichlor 2 lbs @ Amazon => ~$9.00/lb (May 2014)

Keep in mind that Amazon products normally ship free; and that in many parts of the country, you will not have to pay sales tax. Shipping + tax can increase the cost from other suppliers by 15 - 40%, so compare delivered cost, not nominal price.