We aim to characterize the outflow properties of a sample of early Class 0 phase low-mass protostars in Orion first identified by the Herschel Space Observatory. We also look for signatures of infall in key molecular lines. CO $J$=3-2 and $J$=4-3 maps toward 16 very young Class 0 protostars were obtained using the Atacama Pathfinder EXperiment (APEX) telescope. We search the data for line wings indicative of outflows and calculate masses, velocities, and dynamical times for the outflows. We use additional HCO$^+$, H$^{13}$CO$^+$, and NH$_3$ lines to look for infall signatures toward the protostars. We estimate the outflow masses, forces, and mass-loss rates based on the CO $J$=3-2 and $J$=4-3 line intensities for 8 sources with detected outflows. We derive upper limits for the outflow masses and forces of sources without clear outflow detections. The total outflow masses for the sources with clear outflow detections are in the range between 0.03 and 0.16 $M_odot$ for CO $J$=3-2, and in the range between 0.02 and 0.10 $M_odot$ for CO $J$=4-3. The outflow forces are in the range between $1.57times10^{-4}$ and $1.16times10^{-3}$ $M_odot$ km s$^{-1}$ yr$^{-1}$ for CO $J$=3-2 and in the range between $1.14times10^{-4}$ and $6.92times10^{-4}$ $M_odot$ km s$^{-1}$ yr$^{-1}$ for CO $J$=4-3. Nine protostars in our sample show asymmetric line profiles indicative of infall in HCO$^+$, compared to H$^{13}$CO$^+$ or NH$_3$. The outflow forces of the protostars in our sample show no correlation with the bolometric luminosity, unlike those found by some earlier studies for other Class 0 protostars. The derived outflow forces for the sources with detected outflows are similar to those found for other - more evolved - Class 0 protostars, suggesting that outflows develop quickly in the Class 0 phase.
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