The fundamental observables in Cosmology are the late time correlation functions of density fluctuations and gravitational waves, which in turn can be inferred from the wavefunction of the universe (WFU) at the end of inflation. The perturbative computation of the WFU involves integration over the "unobservable" evolution in time, à la the standard in-in computation. Due to the lack of time translation in Cosmology, the procedure becomes quickly intractable at higher orders in perturbation theory. Therefore, in the same spirit as the flat-space amplitude program, it would be of utmost interest if this final WFU can be ``bootstrapped`` by implementing the principles of unitarity, locality and analyticity, directly on the boundary of the quasi-de Sitter universe. In this talk, after reviewing the state-of-the-art Cosmological Bootstrap, I introduce a new set of tools for this program. I first review the Cosmological Optical Theorem that shows how the unitarity of the time evolution is encoded in the coefficients of the WFU. Secondly, I propose a Manifest Locality test that decides whether a given coefficient in the WFU can originate from a (manifestly) local interaction in the bulk. I show the power of these tools by bootstrapping a number of contact and exchange diagrams in the framework of the EFT of inflation.