Many efforts have been done in recent years to probe the gas fraction evolution of massive quiescent galaxies (QGs); however, a clear picture has not yet been established. Recent spectroscopic confirmations at z>3 offer the chance to measure the residual gas reservoirs of massive galaxies a few hundreds of Myr after their death and to study how fast quenching proceeds in a highly star-forming Universe. Even so, stringent constraints at z>2 remain hardly accessible with ALMA when adopting molecular gas tracers commonly used for the quenched population. In this letter, we propose overcoming this impasse by using the carbon [CII] 158 micron emission line to systematically probe the gaseous budget of unlensed QGs at z>2.8, when these galaxies could still host non-negligible star formation on an absolute scale and when the line becomes best observable with ALMA (Bands 8 and 7). So far predominantly used for star-forming galaxies, this emission line is the best choice to probe the gas budget of spectroscopically confirmed QGs at z>3, reaching 2-4 and 13-30 times deeper than dust continuum (ALMA band 7) and CO(2-1)/(1-0) (VLA K-Kalpha bands), respectively, at fixed integration time. Exploiting archival ALMA observations, we place conservative 3sigma upper limits on the molecular gas fraction (fmol=MH_2/Mstar) of ADF22-QG1 (fmol<21%), ZF-COS-20115 (fmol<3.2%), two of the best-studied high-z QGs in the literature, and GS-9209 (fmol<72%), the most distant massive QG discovered to date. The deep upper limit found for ZF-COS-20115 is 3 times lower than previously anticipated for high-z QGs suggesting, at best, the existence of a large scatter in the fmol distribution of the first QGs. Lastly, we discuss the current limitations of the method and propose ways to mitigate some of them by exploiting ALMA bands 9 and 10.