  Is it possible to read off the quantum gravity dual of a CFT directly from
its operator algebra? In this essay, we present a step-by-step recipe
synthesizing results and techniques from conformal bootstrap, topological
symmetries, tensor networks, a novel symmetry-preserving real-space
renormalization algorithm devised originally in lattice models, and the
asymptotics of quantum $6j$ symbols, thereby providing an answer in the
affirmative. Quantum 2D Liouville theory serves as a simple and explicit
example, illustrating how the quantum gravitational path integral can be built
up from local pieces of BCFT correlation functions, which we call the ``BCFT
Legos''. The constructive map between gravity and CFT naturally and explicitly
bridges local geometrical data, algebraic structures, and quantum entanglement,
as envisaged by the $\it{It \, from \, Qubit}$ motto.
