Congrats on the new liner.
You can dose CYA, but it will be hard without a running pump. Keep the CYA off your liner so it doesn't fade & spot your new pretty liner. City water doesn't have any CYA in it so no need to test for it and you know your starting point. As much as you want to get CYA in there, it may be easier to wait for a working pump unless you can let your fill hose run over a sock filled with CYA.
You can dose the chlorine with some bleach to 3ppm in the evening and it should hold overnight. Stir it around with a brush / broom to get it mixed well. That should get you through until you can get your pump installed. On a fresh fill with clean water, not much bad will happen in a couple of days this way.
When you get the pump installed, run it for 30 mins before you grab your water sample. Post your results up here and we can offer advice.