There is no doubt that the Apostle Paul penned the book of Galatians, and many consider it to be his first writing between 47 and 50AD. It had to have been written after the Council in Jerusalem spoken of in Acts 15 which happened in 46AD. That was when the discussion had occurred about if the Gentile grace believers should be required to keep the Law. It would make sense that he wrote this book right after that sometime around the time of Acts 16 when he was in the region of Galatia which was a region that was in Asia Minor (Acts 16:6). Today, it is modern Turkey. Therefore, it had to have been after his first missionary journey and the Jerusalem Council.
The book, just as Acts, must be viewed through the dispensational lens, or it will not make sense and will contradict. I use the word dispensational, because we must see the book for what it is. It is an argument that we are no longer under the dispensation of the law, and to insist so is to pervert the gospel of grace that began with Paul; therefore, he is uniquely our apostle. It is also obvious that conclude that by grace through faith, not of works would be erroneous. Of course, that does not preclude many, quite frankly most, from doing just that today, unwittingly espousing covenant theology.