TL;DR In rough chronological order: Wingfield, Tilden, Vines, ((Crawford)), ((Perry)), Budge, Kramer, (Hoad), Gonzalez/Rosewall/Laver, Borg, Lendl, (Agassi), (Sampras), Federer/Nadal/Đoković. In all, 1 originator + 12 top of the top players/innovators/luminaries + 3+2 honourable mentions.
To start with, "throughout the beginning of time to now," everybody's missing the VIP without whom it would not have happened at all: Walter Clopton Wingfield, the inventor of lawn tennis. He must be #1 on all such lists. The only person who could precede him would be the inventor of réal tennis, but I'm unaware of a single person who could claim to be that.
For the remaining positions (as many as they have to be, 10 is just an arbitrary number), I choose the most prominent champions. Even if their accomplishments are not always directly comparable to today's tennis (focusing on tours vs tournaments, ease of travel, number of matches in Slams, improved technology and support etc.), their achievements were landmarks at the time. Here they are in the order that they come to mind bundled with the most apparent reason why.
The early major champions were in the right place at the right time, but they might not be above the Challenger level today: for example, the second British Open "champion" was just stopping by to pick up the title while being on holiday. Here, the usually improperly used word "winner" is justifiable, just as for the winner of the 1973 edition of the tournament, even though it's not their fault that they got a hollow roster without worthy opposition at the "topmost" level. Also, oops, it was not a proper Open then -- it would take nine more decades of shamateurism until all tennis tournaments would open up. So, no player before the end of the first Great War ranks in.
Once tennis was established globally, Tilden was the first truly outstanding player. He was also a great tactician and innovator, and his fame has brought tennis into the limelight.
The next two plus four that come to mind are the ones who have faced the toughest opposition at the top, with peaks bookended by the peaks of two other greats, incidentally both playing with their non-dominant hand: Rosewall and Nadal, sandwiched between Gonzalez/Laver and Federer/Đoković. All six are formidable champions, their records fill pages, as you all know. I believe the time all three in their respective sets were at the height of their powers have been the two Golden Ages of men's tennis so far, even though I've only experienced the latter.
Besides the only other Calendar Year Grand Slam in 1969 (the four titles in 1962 were amateur level, avoiding contemporary pros and definitely not "grand" even by the standards its time, though many people ignorantly classify the two showings as equivalent), Budge's 1938 CYGS is said to be a roughly comparable achievement. While it was an amateur Slam, turning pro the next year, Budge would hold his own against the other pros of the time very well, while Laver's 1963 was still formative. Almost-honourable mentions go to Crawford, who came within one set of completing an amateur CYGS for the first time in 1933, and Perry, who completed the first amateur Career Grand Slam in 1935.
Statistics show that Borg had the fastest rise to the top, but he severely lacks longevity in comparison to everyone else (except for Budge who was hindered by the War and also his injury sustained in it), so on my list, he only gets an honourable mention. Vines and to a lesser extent Hoad are said to be similar: rose fast, shone bright, gave up relatively early.
Lendl's main contribution, I think, is that pretty much everyone's fitness regime is an updated version of what he (and Navratilova) started doing back in the 80's: even if you're very good but not supremely talented, hard work can fill in the gaps.
I'm not sure if any other players' achievements stack up to be listed at the very top. For example, Sampras and Agassi have, obviously, fabulous résumés, the one with the seemingly-impossible-to-overcome 14 Grand Slams and the other with the Career Grand Slam among other things, but it could be recency bias on my part.
Kramer was definitely one of the top pros, and he was also a prominent tour promoter and instrumental in founding the ATP. Sadly, I only have rudimentary knowledge about his tennis prowess, as he was more the chronicler than the chroniclee, and most of his comments about the other greats read like "he was very very good (... but I was better)" to me, but he definitely was one of the top pros, and he ushered in the serve-and-volley and "percentage tennis" styles in the 50s.
No one else comes to mind with a comparable level of importance.