The demise of Neandertals and the peopling of Europe by anatomically modern humans (AMH) occurred, geologically speaking, in the blink of an eye. While we know that Neandertals and AMH interbred, how and where this interaction occurred remains unresolved. Now that humans can be fingerprinted from the aDNA they left behind in sediments, high-resolution site formation studies are essential to establish microstratigraphic integrity and to reconstruct the human past at finer scales. MATRIX will zoom into the sedimentary matrix at an unprecedented resolution using aDNA, but also proteins and lipids stored in archaeological sediments, in order to: 1) find  the identity of past hominins in well-preserved micro-contexts, 2) reconstruct both their behaviors (diet, use of fire) and environments they lived in, and 3) contribute to rewriting what happened at the time of Neandertal disappearance by integrating high-resolution molecular and microscopic records. We will focus on seven selected sites distributed throughout Europe and with established aDNA preservation. We will assess the microstratigraphy of deposits from ~50 to 40,000 years BP by studying intact archaeological samples in 2D and 3D micromorphological views. We will obtain aDNA data at a micro-scale, and couple it with bone proteins and lipids from organic-rich sediment samples, all extracted from intact micromorphological samples. The project aims to achieve, for the first time, an integration of biological, behavioral, and environmental information of archaeological deposits at a mm- and sub-mm stratigraphic scale. Pioneering the application of microarchaeological techniques linked with contextualized molecular data, while setting a rigorous basis for their interpretation, MATRIX will greatly improve our understanding of the migration of AMH into Eurasia and, eventually, to our inhabiting of the entire world.