  We introduce a comprehensive framework for analyzing finite $N$ lattice
Yang-Mills theory and finite $N$ matrix models. Utilizing this framework, we
examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4
dimensions. The SU(2) Makeenko-Migdal loop equations on the lattice are linear
and closed exclusively on single-trace Wilson loops. This inherent linearity
significantly enhances the efficiency of the bootstrap approach due to the
convex nature of the problem, permitting the inclusion of Wilson loops up to
length 24. The exact upper and lower margins for the free energy per plaquette,
derived from our bootstrap method, demonstrate good agreement with Monte Carlo
data, achieving precision within $0.1\%$ for the physically relevant range of
couplings in both three and four dimensions. Additionally, our bootstrap data
provides estimates of the string tension, in qualitative agreement with
existing Monte Carlo computations.
