We study the molecular gas content of 24 star-forming galaxies at z = 3-4, with a median stellar mass of 10(9.1) M-circle dot, from the MUSE Hubble Ultra Deep Field (HUDF) Survey. Selected by their Ly alpha lambda 1216 emission and H (F160W)-band magnitude, the galaxies show an average < EWLy alpha 0 > approximate to 20 angstrom, below the typical selection threshold for Ly alpha emitters (EWLy alpha 0 > 25 angstrom), and a rest-frame UV spectrum similar to Lyman-break galaxies. We use rest-frame optical spectroscopy from KMOS and MOSFIRE, and the UV features observed with MUSE, to determine the systemic redshifts, which are offset from Ly alpha by = 346 km s(-1), with a 100 to 600 km s(-1) range. Stacking (CO)-C-12 J = 4 -> 3 and [C I]P-3(1) -> P-3(0) (and higher-J CO lines) from the ALMA Spectroscopic Survey of the HUDF, we determine 3 sigma upper limits on the line luminosities of 4.0 x 10(8) K km s(-1)pc(2) and 5.6 x 10(8) K km s(-1)pc(2), respectively (for a 300 km s(-1) line width). Stacking the 1.2 mm and 3 mm dust-continuum flux densities, we find a 3 sigma upper limits of 9 mu Jy and 1.2 mu Jy, respectively. The inferred gas fractions, under the assumption of a "Galactic" CO-to-H-2 conversion factor and gas-to-dust ratio, are in tension with previously determined scaling relations. This implies a substantially higher alpha(CO) >= 10 and delta(GDR) >= 1200, consistent with the subsolar metallicity estimated for these galaxies (12 + log(O/H) approximate to 7.8 +/- 0.2). The low metallicity of z >= 3 star-forming galaxies may thus make it very challenging to unveil their cold gas through CO or dust emission, warranting further exploration of alternative tracers, such as [C II].