Preheat oven to 400 degrees F and line a baking sheet with parchment paper or a non-stick baking mat.
Gently place puffed pastry sheet on the baking sheet and prick with a fork to prevent bubbling. Bake for 12-15 minutes until pastry is slightly golden on the edges. Remove and let cool completely. (The pastry will puff up - you may need to gently flatten once cooled before spreading the cream cheese whipped cream.)
While the pastry is baking and cooling, whip the heavy whipping cream on high-speed in a stand-alone mixer fitted with a whisk attachment or with a hand-held mixer until soft peaks form - careful to not over-whip. Once whipped, place in a bowl and put in the refrigerator.
Next, add the room temperature cream cheese and maple syrup to your mixer bowl (hand-held mixer works too) and whip until smooth, only a few seconds. Then add the whipped cream and mix on low until incorporated. Taste for sweetness - add more maple syrup if you would like, but mix on low-speed to not over-whip the whipping cream.
Once pastry has cooled, spread the whipped cream mixture on top then add sliced peaches. You can drizzle with more maple syrup and sprinkle with cinnamon and thyme. Place in refrigerator to cool slightly then serve immediately. This will keep overnight, but the pastry may be slightly soggy. I suggest serving it sooner rather than later.
You can bake the puffed pastry ahead of time and make the whipped cream/cream cheese mixture ahead of time then assemble before you would like to serve.