global middlewares are triggered before route middlewares in Laravel as you can see in the following source code from Laravel framework:

/**
     * Send the given request through the middleware / router.
     *
     * @param  \Illuminate\Http\Request  $request
     * @return \Illuminate\Http\Response
     */
    protected function sendRequestThroughRouter($request)
    {
        $this->app->instance('request', $request);

        Facade::clearResolvedInstance('request');

        $this->bootstrap();

        return (new Pipeline($this->app))
                    ->send($request)
                    ->through($this->app->shouldSkipMiddleware() ? [] : $this->middleware)
                    ->then($this->dispatchToRouter());
    }

protected $middleware = [
  \App\Http\Middleware\CheckForMaintenanceMode::class,
  \Illuminate\Foundation\Http\Middleware\ValidatePostSize::class,
  \App\Http\Middleware\TrimStrings::class,
  \Illuminate\Foundation\Http\Middleware\ConvertEmptyStringsToNull::class,
  \App\Http\Middleware\TrustProxies::class,
];