I would have to respectfully disagree with Madwil. I would DEFINITELY shock your pool to start. That's the first thing. Shock it to the 10-12 level. Your pH is fine so that's not an issue. I would do that before adding CYA. First things first. And vacuum the pool to waste. I have a robotic cleaner so I run that about 4 times to get the same effect.

Then you can use Trichlor tabs to maintain FC and add CYA, if you have them. The Tabs erode keeping a fairly constant level of FC to offset the lack of CYA. But you'll need to watch your pH and keep a couple of boxes of Borax handy for when the pH drops due to the tabs. If not, you'll need to use bleach and add CYA separately. Always use LESS CYA than you think you'll need. It's easy to add but hard to get rid of when you over-shoot.

Watch your CYA every week and when it hits your target (I recommend 30ppm for spring and early summer, and 50ppm for mid-July and August), stop using trichlor completely and stick to bleach.

I, too, live in NJ and have the same issues (not really problems, just the task you face). That's why by pure dumb luck I've found that CYA of 30ppm for the first half of the season and 50ppm for the second half works well.

BTW, I ALWAYS open to FC=0, and CYA=0. If I can, I open mid April with far less clean up. If I have to wait 2 or 3 weeks (like this year) I have green slime, which is now gone. It was gone, mostly in 2 days.

Carl