Well the Great Burn had nothing to do with Babylon 5 or it's crew. Their mission was originally just to help prevent any further alien-human conflicts like the Mimbari war. As things took shape they went outside their remit to the point that they actually overthrew their 'lawful' government in a military coup, so I suppose in that sense you could say that their actions
did lead indirectly to the Great Burn as it fostered a resentment in those extremist factions ousted in the coup