I would not focus on trying to make it go purple for a few reasons.
number 1 is its a massive waste of energy to install ac just to make it turn colours.
number 2 is that only the fan leaves and some tips of the buds will turn purple, does not penetrate into the nuggets.
number 3, its only a week old. and this is something that gets done in the last few weeks of the plant, if its getting cold every night from a sprout to harvest it will have stunted growth as the purpleing is caused by chlorophyll breakdown and that's need to grow your plants nice and big.
It would be a much better investment into your time and pocketbook to just get a strain that is naturally purple/red.
The idea of using the AC units that runs off of ice is also not ideal. They create an influx of humidity in the air and when you in late flower you do not want extra humidity unless your below 40% RH ambient.
Good Luck!
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