A couple things to consider. By definition, proper curing is the retention of mix water to fuel hydration, the chemical process whereby concrete gains strength. You want to keep this protection in place for a minimum of seven days and ideally closer to 28.
At the same time, this moisture is the enemy of any kind of adhered flooring. Complicating matters more is the weather conditions. Cool weather slows down the strength gain and 'drying' process even more. If you are in a rush to cover the floor, your options don't include anything adhered. I think you are looking at waiting an extended period or using a loose laid option such as RaceDeck.
Give my Guide to Floor Slabs in the link below for some additional thoughts on the process especially placing in cold weather. Good luck with your pour.