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Spectroscopic multiplicity surveys of O stars in young clusters and OB associations have revealed that a large portion ($\sim$ 70%) of these massive stars (M$_{i}$ $\gt$ 15 $M_{\odot}$) belong to close and short-period binaries (physical separation d $\lt$few au). Despite the recent and significant progress, the formation mechanisms leading to such close massive multiple systems remain to be elucidated. As a result, young massive close binaries (or higher-order multiple systems) are unique laboratories to figure out the pairing mechanism of high-mass stars. We present the first VLTI/GRAVITY observations of six young O stars in the M17 star-forming region ($\lesssim$ 1 Myr) and two additional foreground stars. From the interferometric model fitting of visibility amplitudes and closure phases, we search for companions and measure their positions and flux ratios. Combining the resulting magnitude difference with atmosphere models and evolutionary tracks, we further constrain the masses of the individual components. All of the six high-mass stars are in multiple systems, leading to a multiplicity fraction (MF) of 100%, yielding a 68% confidence interval of 94-100%. We detect a total number of 9 companions with separations up to 120 au. Including previously identified spectroscopic companions, the companion fraction of the young O stars in our sample reaches 2.3$\pm$0.6. The derived masses span a wide range from 2.5 to 50 $M_{\odot}$, with a great tendency towards high-mass companions. While based on a modest sample, our results clearly indicate that the origin of the high degree of multiplicity is rooted in their star formation mechanism. No clear evidence for one of the competing concepts of massive star formation (core accretion or competitive accretion) could be found. However, our results are compatible with migration as a scenario for the formation of close massive binaries.