If the police stop you and you take a breath test, any alcohol you drank within the past few hours will show in the test reading. Most people understand that, so they generally avoid driving immediately after drinking.
What many people forget is that it takes time for your body to clear out the alcohol you consume, and the more you drink, the longer it will take, as your body can only process a certain amount per hour.
Hence if the police stop you in the morning, you could still have enough alcohol in your system from the night before to get in trouble.
If it is still in your system, it is probably affecting your driving
The police are allowed to stop you for several reasons. One is if you pass through a sobriety checkpoint. Another is if they see you driving in a way that suggests you might be drunk.
Have you ever seen a colleague struggle through the workday after a big night out? If alcohol can visibly affect their ability to do their job, it can visibly affect your ability to drive, making it more likely the police will pull you over. Remember, they may charge you even if you test under the limit.
Getting pulled over the morning after does not guarantee you will be convicted
There are many ways to challenge a DUI. Just because your drank alcohol the night before does not mean you are guilty. The breathalyzer reading could be wrong. Or maybe the police misinterpreted how you were driving. Perhaps you drove in a stop-start fashion due to mechanical issues rather than alcohol. Be sure to get legal help to examine all defense options if facing DUI charges.