In this paper, we study the spontaneous cortical neuronal network in hopes of finding a reliable indicator of burst initiation pathway, which would allow us to study burst initiation in conjunction with burst propagation in future research. Electrical activity is recorded using a 96-electrode microelectrode array on a weekly batch culture (half of the medium was replaced twice every week). We hypothesize that the first-spike onset sequence, which we call first-spike rank order (FSRO) is a reliable indicator of burst initiation, and verified our hypothesis by studying evoked bursts using rearranged rank probability matrices. Under similar conditions, stimulating the same site reliably reproduces the same FSRO. Spontaneous bursts can be classified based on their FSRO using dendrogram clustering. Bursts with different first-spike sequences showed evidence of sharing common early-to-fire neurons, but early-to-fire neurons only consist of a minority of neuronal activity during burst initiation, which is in partial accordance with existing literature. In the study of early-to-fire neurons, we also noticed that our batch-cultured network did not show clear preburst activity, which may indicate fundamental difference compared to continuous perfusion culture.