In conventional Bardeen-Cooper-Schrieffer superconductors, Cooper pairs of electrons of opposite spin (i.e., singlet structure) form the ground state. Equal-spin triplet pairs (ESTPs), as in superfluid He3, 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 NbSe2, from the noncollinearity between the out-of-plane Ising spin-orbit field (due to the lack of inversion symmetry in monolayer NbSe2) 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 NbSe2 flakes, of 2-25 monolayer thickness, measuring the quasiparticle density of states (DOS) as a function of applied in-plane magnetic field up to 33 T. In flakes ≲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 tunneling spectra, decreases as a function of the applied magnetic field. However, in bilayer NbSe2, close to the critical field (up to 30 T, 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.