Until now, our knowledge of the extragalactic universe at mid-infrared (mid-IR) wavelengths (>5{mu}m) was limited to rare active galactic nuclei and the brightest normal galaxies up to z~3. The advent of JWST with its Mid-Infrared Instrument (MIRI) will revolutionize the ability of the mid-IR regime as a key wavelength domain to probe the high-z universe. In this work we present a first study of JWST MIRI 7.7{mu}m sources selected with >3{sigma} significance from the lensing cluster field SMACS J0723.3-7327. We model their spectral energy distribution (SED) fitting with 13 JWST and Hubble Space Telescope broad bands, in order to obtain photometric redshifts and derived physical parameters for all these sources. We find that this 7.7{mu}m galaxy sample is mainly composed of normal galaxies up to z=4 and has a tail of about 2% of sources at higher redshifts to z~9-10. The vast majority of our galaxies have [3.6]-[7.7]<0 colors and very few of them need high dust extinction values (A_V_=3-6mag) for their SED fitting. The resulting lensing-corrected stellar masses span the range 10^7^-10^11^M_{sun}_. Overall, our results clearly show that the first MIRI 7.7{mu}m observations of deep fields are already useful to probe the high-redshift universe and suggest that the deeper 7.7{mu}m observations to be available very soon will open up, for the first time, the epoch of reionization at mid-IR wavelengths.