At which point in time did the fledgling underground resistance movement erupt into full scale Galactic Civil War and Rebellion?
Answers for both Disney and Legends canonicities desired.
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In Revenge of the Sith, it's explained that a little group of Senators, the Delegation of 2000, were disgusted about the extraordinary powers of Supreme Chancellor Palpatine. We know that Padmé Amidala, Garm Bel Iblis, Mon Mothma and Bail Organa were part of this adventure.
If you consider Star Wars Rebels TV series, it is known that five years before A New Hope and fourteen years after Revenge of the Sith the Rebel Alliance is still a group of little cells, orchestrated by both Bail Organa and former Jedi Ahsoka Tano. They were acting more or less like terrorists.
Considering that, it appears that the first really important military campaign was Operation Skyhook, which is the one figured in A New Hope.
The Galactic Civil War, known as the First Galactic Civil War by the year 43 ABY, was a major galactic conflict fought primarily between the Galactic Empire and the Alliance to Restore the Republic. The Alliance was a rebel faction dedicated to the restoration of the Galactic Republic, the government that the Empire had supplanted at the culmination of the Clone Wars in 19 BBY.
The origins of the conflict could be traced to the Galactic Senate during the final days of the Old Republic, sometime after the end of the Clone Wars, where dissenting and prominent Senators, such as Bail Organa and Mon Mothma, secretly opposed the powers and authority that Supreme Chancellor Palpatine continued to accumulate under the guise of security and war-time measures.
The war did not begin in its real sense, that of an Alliance against the Empire with its goals and ideals laid out for the galaxy, until nearly two decades after the rise of the Empire, when various Rebel leaders signed the Corellian Treaty and issued the Declaration of Rebellion.
(From the Star Wars fandom Legends page for the Galactic Civil War.)
From canon, we know that the movement existed from the very moment the Empire was declared - this was clearly seen in a deleted scene in Revenge of the Sith, with Mon Mothma and friends starting the Alliance (by then, a political movement, rather than an outright insurgency).
As for the actual rebellion, this is clearly outlined in Legends - the Corellian Treaty of 2 BBY was a specific declaration of violent rebellion against the Empire, after a long period of political failure and the long preparation of allies all over the galaxy. It was basically a formal declaration of war, and it rallied many of the individual insurgent cells into one organized rebellion.
Another important point was at the very start of A New Hope, when the Empire dissolved the imperial senate, formally "destroying" the last remnants of the republic - though it really was just a gesture at that point.
In Canon, the Galactic Civil War officially started with the Battle of Scarif:
The Outbreak of War
The Battle of Scarif saw the Rebel Alliance declare open war against the Empire and, though it cost them much of their fleet, it paved the way for their future success.
(Source: Battles that Changed the Galaxy, page 127, section "Galactic Civil War: Introduction")
The same source also lists the Battle of Scarif as the first event in the Galactic Civil War timeline, and lists earlier events from Rogue One in the separate section "Sparks of Rebellion".
The Rebel Alliance had formally existed prior to this, and was founded in 2 BBY, according to the upcoming book Star Wars: Timelines.