Just as humans are different from one another, so are Goa'uld. They have different personalities and strengths. For instance, we see some Goa'uld like Niirti that are very skilled at scientific experimentation. Some are better at scheming and consolidating their power, such as Ba'al.
Ra, then, was better at being cunning, acquiring and expanding his power, and getting the others to see things his way. He played the game of politics with his fellow Goa'uld, and won.
Ra also helped overthrow Sokar during a temporary alliance, as we find out in S2:E18 "Serpent's Song":
TEAL'C:
Sokar is a Goa'uld of ancient times. He once was ruler of the system lords but was defeated by an alliance of Goa'uld many centuries ago. Apophis and Ra were among his conquerors.
His role here shows that he was already among the powerful, but not the most powerful. However, he may have found some way to acquire more of Sokar's resources, or otherwise position himself above the other Goa'uld. Apophis may have been a contender, but somehow fail short. After Ra fell, it's no surprise that Apophis was the first major Goa'uld the Tau'ri encountered.
Part of Ra's rise to power could be attributed to his discover of the Tau'ri. Before humans were used as hosts, Unas were used instead. But, from what we saw of the Unas, the species was not very advanced. They were physically superior to humans, but provided little other benefit: they're technology was was rudimentary even in modern times, and their dexterity seemed low.
Goa'uld sarcophagus could also heal the human hosts from virtually any injury, and even the effects of aging and death (as seen when Ba'al repeatedly killed and revived O'Neill). Unas may not have been able to be healed this way, because their physiology was far different than the Ancient physiology the hijacked technology was meant for. This would have made Tau'ri hosts even more valuable. However, this is never really tested and is speculation (there must have been a reason for abandoning the Unas, though).
Controlling the source of hosts for his species obviously put Ra at a continued advantage. As we saw throughout the series, almost none of the other planets with humans taken from Earth ever reached the population density of Earth itself, even 5,000 years after their discovery. So, even the low population of ancient Earth would have been a considerable advantage over his fellow System Lords.
Once the uprising tossed Ra from Earth, and it's location was lost, it's safe to assume Ra carried over some advantage from previously having a direct line of access between Earth and his other controlled planets.
There's some additional info from an RPG supplement for the official Stargate D20 RPG, called Living Gods: Stargate System Lords. While it wasn't written specifically by any Stargate SG-1/Atlantis writers that I can tell, it was developed in coordination with two MGM employees.
22, 000 B.C. Apep was an "alpha male" of the Goa'uld, and their original leader. He appointed Ra, among others, as his direct reports. During this time period, the Unas are nearly wiped out.
18,000 B.C. Thoth invents the sarcophagus, based on stolen Ancient technology. It extended the life of Unas for a few generations, but not indefinitely. Not, this parts clearly from television canon, because an episode in Season 7 established that Telchak created the first sarcophagus. The RPG was written current up to Season 5 only.
17,400 B.C. After the defeat of Anubis, Ra takes it upon himself to be the new alpha male. Again, this parts from TV canon which says that Ra was acknowledge by the other Goa'uld to be Supreme System Lord, rather than it being forcefully taken.
