Creating shortcut on the home screen through application on install is not possible. There is optional settings in Play Store App to auto create shortcut on install.
Alternatively,you can use below code to create shortcut in OnCreate method of MainActivity:
Require Manifest Permission.
<uses-permission android:name="com.android.launcher.permission.INSTALL_SHORTCUT" />
Use below code to programmatically create shortcut.
Intent shortcutIntent = new Intent();
shortcutIntent.setClassName("<Your app package>", "Class Name");
shortcutIntent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
shortcutIntent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);
Create shortcut itself
Intent addSCIntent = new Intent();
addSCIntent.putExtra(Intent.EXTRA_SHORTCUT_INTENT, shortcutIntent);
addSCIntent.putExtra(Intent.EXTRA_SHORTCUT_NAME, "<Shortcut Name>");
addSCIntent.putExtra(Intent.EXTRA_SHORTCUT_ICON_RESOURCE, Intent.ShortcutIconResource.fromContext(context, R.drawable.ic_launcher);
addSCIntent.setAction("com.android.launcher.action.INSTALL_SHORTCUT");
context.sendBroadcast(addSCIntent);