Flutter provides you the ability to have a splash screen by default but there are a lot of plugins that can do the job. If you don't want to use a plugin for the task and you're worried that adding a new plugin might affect your app size. Then you can do it like this.
FOR Android
Open launch_background.xml then you can put in the splash screen image, or gradient color you want. This is the first thing your user sees when they open your app.
For IOS
Open your app using Xcode, Click on Runner > Assest.xcassets > LaunchImage, You can add the image here. If you want to edit what position launch screen image should take or look like you can edit it on LaunchScreen.storyboard.