We report on recent progress and next steps in the design of the proposed MATHUSLA Long Lived Particle (LLP) detector for the HL-LHC as part of the Snowmass 2021 process. Our understanding of backgrounds has greatly improved, aided by detailed simulation studies, and significant R&D has been performed on designing the scintillator detectors and understanding their performance. The collaboration is on track to complete a Technical Design Report, and there are many opportunities for interested new members to contribute towards the goal of designing and constructing MATHUSLA in time for HL-LHC collisions, which would increase the sensitivity to a large variety of highly motivated LLP signals by orders of magnitude. Comment: Contribution to Snowmass 2021 (EF09, EF10, IF6, IF9), 18 pages, 12 figures. v2: included additional endorsers. v3: updated affiliations. v4: added missing contributors as authors