Sounds like you're good to go!
You'll need to get some stabilizer in there. If you have a Sams Club nearby, and have access, one easy way is to buy their 24lb box of dichlor shock, for about $2.50/lb (at least, that's what they charge here). Almost every other retailer of dichlor, including Walmart and Costco, is selling a variety of hodge-podge blends, that should be avoided! You can check at HomeDepot and Lowes, but you have to be an expert label inspector, to avoid the stuff!
Anyhow, 24lbs of dichlor will add about 50 ppm of chlorine, and about 45 ppm of stabilizer to your pool.
If you can't buy from Sams, you can usually find unblended (100%) stabilizer locally, though it's often quite expensive. 1 lb will add about 4 ppm of CYA to your pool, so you probably want at least 10 lbs.
As an alternative, you can get trichlor tabs from Sams in a 40# bucket, and use them in a floater or your skimmer, along with bleach to stock. Again, most other retailers are selling hodge-podge trichlor, often with copper (= stains & green hair) added.
If you can't find what you need locally, you can get the products from Amazon:Kem-Tek Dichlor 22.5 lbs @ AmazonRegardless, if you use bleach for shocking, you should be able to avoid having your CYA get too high, over the course of the summer.
Kem-Tek 3" Trichlor 35lbs @ Amazon
Kem-Tek 879 Pool Floating Tablet Dispenser
Best wishes.
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