Certified GKH Gardening Expert
You can take cuttings at any time, if you are planing to root these indoors. Just make sure that the plants are not flowering when you take the clones, as flowering hormone tends to inhibit rooting hormone.
If you intend to root these cuttings outdoors, then make sure that you take the cuttings during the rainy season to ensure that they receive water to strike.
This article will help: https://www.gardeningknowhow.com/ornamental/flowers/begonia/begonia-propagation.htm