Student teaching assistants (TAs) are essential contributors to CS education and are often the first point of contact for many students. Given increasing evidence that student achievement is directly correlated to a positive classroom climate, an effective TA must possess not only strong domain and pedagogical skills, but also the skills necessary to maintain an inclusive, welcoming, and supportive classroom environment. Our view is that there is no meaningful separation between pedagogical and climate skills: rather than ``compartmentalizing'' climate into specific workshops or modules of a course, our semester-long required TA preparation course treats classroom climate as a lens through which traditional pedagogical skills are viewed, such as giving presentations that encourage participation, creating equitable assessments, and creating successful student groups by fostering belonging. We describe a climate-first, scalable, modular TA training curriculum with open-source and curated teaching materials, suitable for in-person or remote instruction, that serves hundreds of first-time TAs each year, and which student feedback suggests is meeting our goals.