Since Rafa was the last guy to do this, it's worth reviewing his career the year it happened: 2005. Here are a few excerpts from his Wikipedia page:
"2005: First Grand Slam title
At the 2005 Australian Open, Nadal lost in the fourth round to eventual runner-up Lleyton Hewitt. Two months later, Nadal reached the final of the 2005 Miami Masters, and despite being two points from a straight-sets victory, he was defeated in five sets by world No. 1 Roger Federer. Both performances were considered to be breakthroughs for Nadal.
He then dominated the spring clay court season. He won 24 consecutive singles matches, which broke Andre Agassi's Open Era record of consecutive match wins for a male teenager. Nadal won the Torneo Conde de Godó in Barcelona and beat 2004 French Open runner-up Guillermo Coria in the finals of the 2005 Monte Carlo Masters and the 2005 Rome Masters. These victories raised his ranking to world No. 5 and made him one of the favorites at his career-first French Open. On his 19th birthday, Nadal defeated Federer in the 2005 French Open semifinals, being one of only four players who defeated the top-seeded player that year (along with Marat Safin, Richard Gasquet, and David Nalbandian). Two days later, he defeated Mariano Puerta in the final, becoming the second male player after Mats Wilander to win the French Open on his first attempt. He also became the first teenager to win a Grand Slam singles title since Pete Sampras won the 1990 US Open at age 19. Winning the French Open improved Nadal's ranking to world No. 3.
Both Nadal and Federer won eleven singles titles and four ATP Masters Series titles in 2005. Nadal broke Mats Wilander's previous teenage record of nine in 1983. Nine of Nadal's titles were on clay, and the remainder were on hard courts. Nadal won 79 matches, second only to Federer's 81. Nadal won the Golden Bagel Award for 2005, with eleven 6–0 sets during the year. Also, he earned the highest year-end ranking ever by a Spaniard and the ATP Most Improved Player of the Year award."
He was having quite a year. It wasn't only that he won a GS as a teenager; he was winning a lot, his ranking was quickly rising near the top, he was beating the best players on the planet.
I post this not to turn it into a Nadal thread, but to point out the degree of accomplishments surrounding that initial GS win. It's not a must, of course, but it's likely that the next guy to win a GS as a teenager will need to be having a highly successful year -- and that's what I don't see.
Sure, we can hang our hopes on some of the young guns, such as Coric, Zverev, or Kokkinakis -- and I hope they do win GSs -- but none of them are having even close to the level of success Nadal was having at their age.