This is quite impossible to tell you the exact time. It does all depend on your injury and how do you manage your injury after that. I would like to give you some tips. If you follow those tips then it would help you to heal your injury faster.
• First of all try and keep your wrist supported when you sleep- a good trick is to lie on your good side with the arm draped over a pillow, one that is perpendicular to your body.
• Warmth can sometimes ease the pain a little-be careful to not make the swelling worse, or to have too hot a heat source.
• Keeping your wrist elevated, in a sling or across your chest while sitting.
• Try to keep the arm elevated above the heart in moments of severe pain. This reduces blood flow to the wrist and relieves the pain and swelling a little.
• Do not try to lift or carry things with your injured arm- it may seem light, but it will do damage to your arm! Especially in the early stages.
• Do not bash your cast or stick things down your cast such as a ruler.
Those are just simple tips from my past experience. I am not a doc. While lifting if you feel slight problem then it is advised that you need to make an appointment with your doc.