You can start the cutouts anytime. If you want them to be a little pliable when you put them on the cake, just cover them with plastic wrap until you're ready to use them. If you want them to be dry and hold a shape, don't cover them. Just make sure they are not in sunlight or they will fade.
I've started making fondant and gumpaste figures and cutouts over the weekend for a cake that won't be decorated until the 21st.
I place my cut-outs on a cookie sheet lined with plastic wrap. I cover each row with wax paper then seal them up with a top layer of plastic wrap. I've had success freezing them and letting them return to room temp. (while still covered), they stay soft. HTH
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