There are different review processes per deploying channel. For example, Apple often takes 1 to 4 weeks to review the app before allowing it on their app stores. On the other hand, Google often takes hours to review apps on the Play Store. If you are new to the store, it often takes an extra week to get familiar with its configuration tool. So, be ready 4 weeks in advance if you need to push the game on the app stores to a deadline, such as a client project.
Note
We didn't go through the process of uploading our game to app stores because their configuration and store listing may change over time. The important thing is to have all the material and target builds ready. With all the material ready, uploading and configuring for each store shouldn't be a burden.