  We investigate the lattice relaxation effect on moir\'e band structures in
twisted bilayer MoTe$_2$ with two approaches: (a) large-scale plane-wave basis
first principle calculation down to $2.88^{\circ}$, (b) transfer learning
structure relaxation + local-basis first principles calculation down to
$1.1^{\circ}$. Two types of van der Waals corrections have been examined: the
D2 method of Grimme and the density-dependent energy correction. We note the
density-dependent energy correction yields a continuous evolution of bandwidth
with twist angles. Including second harmonic of intralayer potential/interlayer
tunneling and the strain induced gauge field, we develop a more complete
continuum model with a single set of parameters for a wide range of twist
angles, \textcolor{red}{ and perform many-body simulations at $\nu=-1,-2/3,
-1/3$. We further identify a series of $C=1$ Chern bands around $2^{\circ}$
from Wilson loop and edges state calculation, which serves as the foundation
point for even-denominator non-Abelian states.
