  In conventional Bardeen-Cooper-Scrieffer (BCS) superconductors, Cooper pairs
of electrons of opposite spin (i.e. singlet structure) form the ground state.
Equal spin triplet pairs (ESTPs), as in superfluid $^3$He, are of great
interest for superconducting spintronics and topological superconductivity, yet
remain elusive. Recently, odd-parity ESTPs were predicted to arise in
(few-)monolayer superconducting NbSe$_2$, from the non-colinearity between the
out-of-plane Ising spin-orbit field (due to the lack of inversion symmetry in
monolayer NbSe$_2$) and an applied in-plane magnetic field. These ESTPs couple
to the singlet order parameter at finite field. Using van der Waals tunnel
junctions, we perform spectroscopy of superconducting NbSe$_2$ flakes, of 2--25
monolayer thickness, measuring the quasiparticle density of states (DOS) as a
function of applied in-plane magnetic field up to 33T. In flakes $\lesssim$ 15
monolayers thick the DOS has a single superconducting gap. In these thin
samples, the magnetic field acts primarily on the spin (vs orbital) degree of
freedom of the electrons, and superconductivity is further protected by the
Ising field. The superconducting energy gap, extracted from our tunnelling
spectra, decreases as a function of the applied magnetic field. However, in
bilayer NbSe$_2$, close to the critical field (up to 30T, much larger than the
Pauli limit), superconductivity appears to be more robust than expected from
Ising protection alone. Our data can be explained by the above-mentioned ESTPs.
