The partisan conflict between Kansas and Missouri didn't begin with the Civil War; its origins came a decade earlier, with the Kansas-Nebraska Act of 1854. The act stipulated that Kansas would be admitted to the Union as a state, but its own citizens would determine whether or not it would allow slavery - this principle was known as "popular sovereignty", espoused by Senator Stephen Douglas and supported by Missouri Senator David Atchison.

Once this principle was established, pro-slavery advocates from Missouri, derisively known as "border ruffians" or "pukes", began flooding across the border to vote a government into power that would draft a state constitution permitting slavery. In response, anti-slavery forces - including abolitionists from New England - sponsored the migration of anti-slavery, or "free-soiler" migrants who would elect a government that outlawed slavery.

The two groups of migrants elected two rival legislatures that both claimed jurisdiction over Kansas - with one pro-slavery capital in Lecompton and an anti-slavery capital in Topeka. The President, Franklin Pierce, recognized the Lecompton government - but that did not resolve the matter.

As free-soilers and border ruffians vied for legitimacy, the conflict turned violent: Horace Greeley called the civil strife between pro- and anti-slavery camps "Bloody Kansas". In November 1856, the so-called Wakarusa War erupted near the free-soiler stronghold of Lawrence, leading to the killing of Charles Dow (originally from Ohio) by Franklin Coleman (originally from Virginia) over a land dispute, and the murder of free-soiler Thomas Barber near Lawrence in December. In the ensuing months, the scale of violence grew larger, including the Pottawatomie Massacre, in which John Brown and his sons entered a pro-slavery settlement and murdered five men. Eventually, federal troops were sent to Kansas to keep the peace, but by the end of the decade more than fifty people had been killed through political violence.

When the Civil War broke out in 1861, it both rekindled and exacerbated the tensions between Missourians and Kansans that had developed during the 1850s. By this time, Kansas was securely held by anti-slavery forces, and the population of the territory - which became a state in January 1861 - was strongly pro-Union.

Early in the war, General James Lane led a brigade of Kansas troops into Missouri, laying waste to the town of Osceola in September 1861. Many of the men in Lane's ranks viewed the attack on pro-Confederate forces in Missouri as a kind of payback for the strife of the previous decade. The troops looted the town, then set it ablaze, killing a number of civilians in the process. At the same time, slaves in Missouri fled to Union lines, and Lane and other Union generals refused to return them to their owners. Pro-Confederate Missourians viewed this as an attack on their property rights, leading them to stage raids and robberies of their own against Unionists in both Missouri and Kansas as a kind of vengeance - most notably those led by William Quantrill.

So you could say that the Missourians threw the first punch before the Civil War through their actions in Bleeding Kansas, but the first real act of aggression against civilians during the war itself was by the jayhawkers in the service of General James Lane.

BTW, this short film provides an excellent introduction to the "border war" between Kansas and Missouri: https://youtu.be/T8MNuXM6UQE

For a much more detailed and nuanced discussion of Bleeding Kansas than I've provided here, I'd also recommend the blog of AskHistorians contributor u/freedmanspatrol: https://freedmenspatrol.wordpress.com/