In order to better understand the role of high-mass stellar feedback in regulating star formation in giant molecular clouds, we carried out a Hubble Space Telescope (HST) Treasury Program Measuring Young Stars in Space and Time (MYSST) targeting the star-forming complex N44 in the Large Magellanic Cloud (LMC). Using the F555W and F814W broadband filters of both the ACS and WFC3/UVIS, we built a photometric catalog of 461,684 stars down to $m_mathrm{F555W} simeq 29$ mag and $m_mathrm{F814W} simeq 28$ mag, corresponding to the magnitude of an unreddened 1 Myr pre-main-sequence star of $approx0.09$ $M_odot$ at the LMC distance. In this first paper we describe the observing strategy of MYSST, the data reduction procedure, and present the photometric catalog. We identify multiple young stellar populations tracing the gaseous rim of N44s super bubble, together with various contaminants belonging to the LMC field population. We also determine the reddening properties from the slope of the elongated red clump feature by applying the machine learning algorithm RANSAC, and we select a set of Upper Main Sequence (UMS) stars as primary probes to build an extinction map, deriving a relatively modest median extinction $A_{mathrm{F555W}}simeq0.77$ mag. The same procedure applied to the red clump provides $A_{mathrm{F555W}}simeq 0.68$ mag.
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