The time it takes to master the game is relative to how much you play, whether or not you take lessons, whether you learn and practice both the mechanical and mental sides of the game and, most importantly, your definition of the word “master”.
“Holes gone wild” are a part of the game. Even professional golfers experience holes similar to the one you described. They can occur at any time, including tournament play in front of many fans. For instance, during the 2018 Masters Tournament at Augusta National, Sergio Garcia made a score of 13 on the 15th hole. A video of Sergio playing the 15th hole is available online. His calm demeanor in an after-game interview indicates one reason for his success as a golf pro.
Throughout the history of the PGA Tour there have been 27 holes in which a pro has carded a 13 or worse on a single hole. There is even a name, “Archaeopteryx”, given to a score of 15 or more over par on a single hole. The name Archaeopteryx derives from the name of a pre-historic bird. The bird may be extinct, but the scores are still cited.
I believe your tears and feelings of frustration may be coming from underlying thoughts similar to, “I’ll never learn this game, I’m wasting my time, I’m stupid, I’m a failure, I’m embarrassed, I’m going to quit.”
I offer you replace these types of thoughts with ones that serve you better and won’t lock in negative feelings of frustration, such as, “Difficult holes are part of the learning process, meeting challenges is how I learn, I’m getting in my bunker practice today, even the pros have high scoring holes at times, I’m determined to play this game, no matter what it takes.” A favorite thought of mine for neutralizing my feelings about a situation is, simply, “How curious.”
Notice how your feelings change when you change your thoughts and perspective. Your most effective thoughts will be the ones you create, you can believe, and that resonate with you.
To my knowledge there is no specific time for mastering the game of golf. Golf great Arnold Palmer says, “The whole secret to mastering the game of golf—and this applies to the beginner as well as the pro—is to cultivate a mental approach to the game that will enable you to shrug off the bad days, keep patient and know in your heart that sooner or later you will be back on top.”
You will know when that time arrives for you. Until then, may you enjoy your time on the course, no matter the curious challenges you can expect to meet.