The 2023 7.8 southeast Türkiye earthquake was recorded by an unprecedentedly large set of strong‐motion stations very close to its rupture, opening the opportunity to observe the rupture process of a large earthquake with fine resolution. Here, the kinematics of the earthquake source are inferred by finite‐source inversion based on strong‐motion records and coseismic offsets from permanent Global Navigation Satellite Systems stations. The strong‐motion records at stations NAR and 4615, which are the closest to the splay fault (SPF) where the rupture initiated and which were previously interpreted to contain the signature of supershear rupture speeds, are successfully modeled here by a subshear rupture propagating unilaterally to the northeast. Once the rupture on the SPF reaches the east Anatolian fault (EAF), it propagates on the EAF bilaterally, extending about 120 km northeast and 180 km southwest. To the south, the depth extent of the rupture decreases, as it passes a bend of the EAF. Although the rupture velocity remains globally subshear along the EAF, we identify three portions of the fault where the rupture is transiently supershear. The transitions to supershear speed coincide with regions of reduced fault slip, which suggests supershear bursts generated by the failure of local rupture barriers. Toward the southwest termination, the rupture encircles an asperity before its failure, which is a feature that has been observed only on rare occasions. This unprecedented detail of the inversion was facilitated by the proximity to the fault and the exceptional density of the accelerometric network in the area.