Hi and welcome to the forum! We will need a complete set of water testing results to be able to do a good job of helping you. We recommend the Taylor K-2006 or 2006C. You can order it from Amazon through the link in my signature, and by doing so, the Pool Forum makes a little money, too!
Most important, is to raise your pH. Any reading below 7.0 is acidic and can damage your pool. Test kits cannot differentiate below 6.9, so your pH may actually be lower than that. You can use 20 Mule Team Borax (laundry aisle at Walmart) to raise the pH. Start with adding a half a box slowly into the skimmer while the pump is running, breaking up any clumps. After a few hours, retest and redose as needed until you get to 7.4-7.6 although anywhere from 7.2-7.8 is ok.
To clear the algae, test as many times a day as you can, a minimum of twice and three times or more is even better, and each time, add enough bleach to get back up to shock level. If you have no CYA as I assume since you have just freshly filled your pool, a shock level of around 12ppm should be fine. In a 27K pool, each quart of 6% bleach will add approximately 0.5ppm of chlorine. Once you can go from sundown one evening from sunup the next morning without losing more than 1ppm of chlorine, you can assume the algae is dead. Run the pump 24/7 while you are trying to clear the pool and allow your filter to do its job of filtering out the dead algae. You may need to clean your cartridge periodically as it filters out the dead algae.
(By the way, it is OK to add doses of Borax and bleach at the same time with no problems. I do so all the time.)
What type of pool is this -- vinyl liner, gunite, fiberglass?
Another idea -- you could use dichlor powder to shock with for awhile if you currently have no CYA. Dichlor will add CYA at the same time as chlorine. But, keep an eye on the CYA level if you do use it. You will want around 40ppm of CYA and once you get to that level, you'll want to either switch to bleach or maybe Cal-Hypo for your source of chlorine.
Repost if you have further questions.
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