Napoleon was lucky to be born when he was:
He was a 20-year-old lieutenant in 1789 when the revolution broke out, too young to take any significant part in the rapid escalations of the years of attacking the king, the fear of emigré aristocrats, the paranoia of internal enemies and the resulting murderous purges. He wasn’t high enough in the aristocracy to have privileges to lose and wasn’t tempted to emigrate; and since two-thirds of the officers did emigrate, there were plenty of vacancies for young officers, especially after the army began to expand in 1793. Artillery was an unfashionable and low-ranking branch, but it was becoming the determining force on the battlefield, hence just the right location to make one’s reputation.
But an officer had to get a command in order to make one’s reputation, and in the situation of revolutionary upheaval, that took politics and network connections. Napoleon got the jump on other officers his age, because he could go back to Corsica and play the big fish in a small pond. He could have joined the local independence movement (its leader was his youthful hero), but once on the spot he found he made a bigger splash, and had more room for action, if he led the pro-French reformers. This brought him favorable notice from delegates of the central government as an energetic and reliable local follower. Playing on the periphery but with useful connections to the center, Napoleon was ready to try a bigger stage.
The danger was that 1793-4 was the period when paranoia and political killings were at their height. The royal family was executed January 1793; Marat assassinated in July; Hébertists and Dantonists fell to Robespierre in spring 1794. Top contenders for power were killing each other. Napoleon was far enough down not to be a target. By the time he made enough military reputation to become a political figure, public mood had shifted to weariness with the violent struggles of revolutionary factions. There was a structural opportunity to play the restorer of order; and it was in this role that Napoleon was initially welcomed.
Thus, a general theory of political luck: What appears fortuitous from the point of view of a particular person, is predictable when seen in terms of structural locations and structural change. It is a matter of reversing the gestalt.
Leading political actors in a period of violent struggle are going to knock each other off. In France, once the royalists were gone, the radicals turned against the moderates; and when they were gone, turned against each other. Eventually when most people are exhausted, there is room for an outsider detached from the ideologically polarized factions to act as peace-maker, establishing a more stable regime. If the structural bases for contending forces are still strong, this outside restorer of order will have opposition that tends to provoke an authoritarian solution; but the restorer will have support in public opinion, in the time-period when they are tired of seemingly endless ideological projects and violent strife. Such a detached outsider cannot be entirely without network connections, but they must be distant and flexible enough so that he is not brought down by old faction struggles. In other words, the situation will select someone like Napoleon in terms of age, peripheral sphere of activity, and multi-sided connections with the center.