But until last month he had also never won a major despite reaching the ten semi-finals since 2020 and the final in each of Melbourne, Paris and New York.
Now, though, he is the newly-crowned French Open champion and the German hopes the confidence his enhanced status engenders leads to a long-desired breakthrough at Wimbledon.
The world No.3 was rarely stretched in beating France's unseeded Valentin Royer 6-1 6-3 7-6 (7-3) on Thursday (Friday AEST) to move into the third round.
"For two-and-a-half sets, I played an almost perfect match but I lost focus and concentration," Zverev said after his 50th tour-level match win on grass.
"He made it interesting, but I'm happy to be through in straight sets. Even though I love to play here, it's nice to win easier in the beginning of the week.
"I'm not old yet, but I'm getting to an age where you need to save energy," the 29-year-old added.
"It builds confidence to win easily, especially in Wimbledon. I love this tournament but I'm waiting for a big result.
"If I play like this it can happen this year. This year I'm coming in as Roland Garros champion. I think the mindset is just very different."
Zverev now plays American Marcos Giron, who also beat French opposition in Quentin Halys 7-6 (7-5) 6-3 6-4.
Further down the line Zverev is scheduled to meet Czech 13th-seed Jiri Lehecka, who beat Alex Molcan 6-3 6-2 6-4, then, in what would be Zverev's first Wimbledon quarter-final, last year's semi-finalist Taylor Fritz.
The American sixth seed defeated compatriot Patrick Kypson 6-2 6-2 7-5 and now plays Italy's Lorenzo Sonego, who put out Canada's Gabriel Diallo.
Then -- and it remains a long way off for both men -- it would be Alex de Minaur for Zverev in the semi.
Two seeds remain in de Minaur's quarter of the draw after ninth-seed Flavio Cobolli beat Australia's James Duckworth and 19th seed Karen Khachanvov sent home Yannick Hanfmann.
But the real threat comes without seeded status. Matteo Berrettini beat de Minaur in straight sets three years ago and his 6-4 7-5 3-6 6-3 defeat of 20th seed Arthur Fils confirmed the injury-dogged 2021 finalist remains a potent force on grass.
So does Grigor Dimitrov, a semi-finalist here 12 years ago. Last year he had eventual winner Jannik Sinner on the ropes when his pectoral muscle tore -- but he's back, and he's still got it, as 15th seed Jakub Mensik discovered under the No.1 Court roof, going down 7-6 (7-5) 4-6 7-5 6-3 to the Bulgarian wildcard.
Berrettini, 30, and Dimitrov, 35, now meet in the most keenly-awaited tie of the third round. If de Minaur keeps winning he will probably face one of them in the quarter-final. It won't be easy.
8°C