The aim of CeNTREX (Cold Molecule Nuclear Time-Reversal Experiment) is to search for time-reversal symmetry violation in the thallium nucleus, by measuring the Schiff moment of
205Tl in the polar molecule thallium fluoride (TlF). CeNTREX uses a cryogenic beam of TlF with a rotational temperature of 6.3(2) K. This results in population spread over dozens of rotational and hyperfine sublevels of TlF, while only a single level is useful for the Schiff moment measurement. Here we present a protocol for cooling the rotational and hyperfine degrees of freedom in the CeNTREX beam, transferring the majority of the Boltzmann distribution into a single rotational and hyperfine sublevel by using a single ultraviolet laser and a pair of microwave beams. We achieve a factor of
20.1(4) gain in the population of the
J=0,
F=0 hyperfine sublevel of the TlF ground state.
We present a hyperfine-resolved state preparation scheme for thallium fluoride (TlF) molecules based on microwave-driven adiabatic passage (AP) in a spatially varying electric field. This method enables efficient and robust population transfer between selected
∣J,mJ=0⟩ hyperfine sublevels of the
X1Σ0+ ground state in a cryogenic molecular beam, a key requirement for the CeNTREX search for nuclear time-reversal symmetry violation. Two sequential stages of AP are implemented. The first transfers population from
J=0 to
J=1 at a local field of
173 V/cm, and the second transfers from
J=1 to
J=2 at
110 V/cm. Transfer efficiencies are quantified through laser-induced fluorescence, and accounting for residual population in excited rotational levels after a prior stage of rotational cooling. We achieve state transfer efficiencies of
0.92(6) and
1.05(5) for the first and second states of AP, respectively. This corresponds to a total efficiency of
0.97(8) for population transfer from
J=0 to
J=2. These results demonstrate robust and high-fidelity preparation of specific rotational/hyperfine states in TlF.