Its important to note that if you have only just created a Google Smart Shopping campaign then it can take upwards of 15 days or more for it to start serving ads.
This is generally due to the following:
Learning Phase: Smart Shopping campaigns start out in what is called "Learning Phase" where Google's machine learning is adapting to search trends and audiences. This is why Google states that it can take upwards of 15 days for these campaigns to begin running.
Your Smart Shopping campaign could also not be serving ads because:
Remarketing Audience Too Small: You may note a notification directly in Google Ads (see below image). Smart Shopping campaigns in Google Ads automatically attach Remarketing Audiences and can only begin serving ads after at least 100 active users are collected in a particular audience.
If this is the case, you can view the current Audience sizes in Google Ads by opening up Tools & Settings > Shared Libary > Audience manager: