Verifique o banco de dados se existe usando Laravel

namespace App\Http\Controllers;

use Illuminate\Support\Facades\DB;

class Testing extends Controller
{
   public function get()
   {
        $query = "SELECT SCHEMA_NAME FROM INFORMATION_SCHEMA.SCHEMATA WHERE SCHEMA_NAME =  ?";
        $db = DB::select($query, [$your_database_name]);
        if (empty($db)) {
            echo 'No db exist of that name!';
        } else {
            echo 'db already exists!';
        }
   }
}