It is possible to start an appium server programmatically. There are multiple ways:
Method 1: Start Appium server using AppiumDriverLocalService
Method 2: Using Appium.js with Node.exe (opening GUI version of Appium using code)
Method 3: Start Appium server using Command Prompt
Generally the commands that are being entered to the command prompt are written in note pad and it is saved with .bat extension and you can click the bat file.