The Galaxy Evolution Exporer (GALEX) has performed unprecedented imaging surveys of the Magellanic Clouds (MC) and their surrounding areas including the Magellanic Bridge (MB) in near-UV (NUV, 1771-2831AA) and far-UV (FUV, 1344-1786AA) bands at 5 resolution. Substantially more area was covered in the NUV than FUV, particularly in the bright central regions, because of the GALEX FUV detector failure. The 5$sigma$ depth of the NUV imaging varies between 20.8 and 22.7 (ABmag). Such imaging provides the first sensitive view of the entire content of hot stars in the Magellanic System, revealing the presence of young populations even in sites with extremely low star-formation rate surface density like the MB, owing to high sensitivity of the UV data to hot stars and the dark sky at these wavelengths. The density of UV sources is quite high in many areas of the LMC and SMC. Crowding limits the quality of source detection and photometry from the standard mission pipeline processing. We performed custom-photometry of the GALEX data in the MC survey region ($<15^{circ}$ from the LMC, $<10^{circ}$ from the SMC). After merging multiple detections of sources in overlapping images, the resulting catalog we have produced for the LMC contains nearly 6 million unique NUV point sources within 15$^{circ}$ and is briefly presented herein. This paper provides a first look at the GALEX MC survey and highlights some of the science investigations that the entire catalog and imaging dataset will make possible.