The most reliable evidence that answers your question is
Milo of Croton (Croton was a town in southern mainland Italy). (
Vide infra for details.)
The Olympics are the best, earliest extant records of competitive combat. (There is evidence of the Minoan & Mycenaean period, but this is limited to the media that survived the Santorini super volcanic eruption that obliterated the ancient island of Thera, being a few potsherds and a couple of incomplete mosaics,
vide infra).
An Athlete (
άθλητὴς competitor) sought dominance and winner-take-all glory (
τὸ ἄθλον the prize) in
ὁ ἄθλος (the competition), signified by the wreath (the Greek word transliterated as
stephanos means a diadem twined from a wreath).
Originally the Archaic Greeks competed in athletics (
γύμνικος ἄγων), and later equestrian (
ἵππος ἄγων) races were added.
Wrestling (
πάλη) was contested first at the 18th Olympiad, 708BCE, and also added to pentathlon, probably because it required skill as well as brute force (hence the Epic fight between Ajax & Odysseus, from the
Iliad).
Boxing was introduced 23rd Olympiad, 688BCE, wherein the fighters wore leather bindings plaited together on the hands (gloves
ἵμαντες) and sometimes ear protection
ἄμφωτιδες. The first contest was won by Onomastos of Smyrna, who also wrote the rules (for subsequent bouts).
The third competition was a mixed martial arts competition called the pankration (
πάνκρατιον = "all-power / -victory"), which first appeared in the 33rd Olympiad, 648BCE, with the boys' competition beginning in 200BCE.
All three combat sports took place on a
σκάμμα of dug-up (soft) ground, probably in the palaistra (
πάλαιστρα, though there is some doubt and of course this may have changed over the centuries), and not in the gymnasium (
γύμνασιον literally the "place for naked exercise").
The chief
ἄλυταρχης of the officials (the
μάστιγοφοροι) determined if a competitor fell, indicated by the impression left in the sand (the arena on which they fought).
In the case of an odd number of competitors, one received (by drawing lots) a first-round bye
ἄκονιτι ("dustless",
i.e., without the dust used in competition, since the competitors fought covered in oil &
κόνις, which is not the sand —
ψάμμος— they stood on).
Milo son of Diotimus (who also led the forces of Croton to defeat the city of Sybaris, 510BCE), has been likened to the modern Russian Greco-Roman wrestler Alexander Karelin, was a giant who won his first of six competitons in the boys’ (either 540 or 536BCE), and was runner-up at the seventh occasion to a fellow Croton, Timasitheus.
Stories tell that he carried his own statue into the Altis (sacred grove); he could hold a pomegranate in his hand without damaging it, whilst preventing any others from taking it; he would stand on an oiled discus and prevent anyone from dislodging him; and another party trick was to snap a cord using just the vasodilation of the arteries in his neck (Pausanias,
Description of Greece, 6.14.5–8).
Theagenes of Thasos, son of Timosthemnes, was champion of boxing, undefeated for 22 years, beginning at the 75th Olympiad in boxing, 480BCE, with over 1000 victories.
Other Details
Once victory was posthumously awarded to Arrhachion; whilst being held in a choke he managed to dislocate his opponent’s toe, who surrendered, but Arrhachion passed out from the stranglehold and died.
Pausanius (writing in C2CE,
Description of Greece, 5.8.6–5.9.1) tells the first (still extant) recorded Olympics occurred 776BCE (just the sprint). Writing a century later (
i.e., about a millennium afterwards), Philostratus (
Gymnasticus, 9) wrote the Spartans invented boxing to help their helmet-less combat (only carrying a shield and armour into battle as a hoplite) only to later abandon it because a competitor might have to submit (being too shameful for Sparta), though he also said it reached the barbarian
Βέρβρυκες tribe of Mysia (north-western modern Turkey).
But the Minoan fresco (
c.1650BCE) & Hagia Triada rhyton (a drinking horn from Crete, dated
c.1550BCE), both depict two boys boxing, from the island of Thera (destroyed when the Santorini volcano erupted,
circa 1500BCE).
According to
this website, the handsome boxer Melankomas, from Caria (west-coastal modern Turkey), was undefeated throughout his career — yet he never once hit, or was hit by, an opponent; defending himself from the blows of the other boxer, he never attempted to strike the other man; won the 207th Olympiad boxing tournament.
Diagoras of Rhodes and his family are remembered as the most successful dynasty. Diagoras won the boxing 464BCE; his sons and grandsons also became boxing and pankration champions; his sons Damagetos & Akousilaos, after winning the 83rd Olympiad, lifted their father on their shoulders to share their victory with Diagoras.
Separately, the race in armour
ὅπλιτοδρομας (but without weapons) completed the competition, from the 65th Olympiad, 520BCE, by signalling the end of the truce
ἔκεχειρα.
Athletic heroes, in Walter Burkert's supplemental definition of a hero, are “a deceased person who exerts from his grave a power for good or evil and who demands appropriate honour”.
Reference
Alan Beale (Cambridge, 2011),
Greek Athletics & the Olympics, specifically chapter 8,
Athletes, pp.140
ff.
edits: syntax