We identify a point-symmetric morphology of three pairs of ears/clumps in the core-collapse supernova remnant (CCSNR) Puppis A, supporting the jittering jets explosion mechanism (JJEM). In the JJEM, the three pairs of jets that shaped the three pairs of ears/clumps in Puppis A are part of a large set, about 10–30 pairs of jets, that exploded Puppis A. Some similarities in morphological features between CCSNR Puppis A and three multipolar planetary nebulae considered to have been shaped by jets solidify the claim for shaping by jets. Puppis A has a prominent dipole structure, where one side is bright with a well-defined boundary, while the other is faint and defused. The neutron star (NS) has a natal kick velocity in the opposite direction to the denser part of the dipole structure. We propose a new mechanism in the frame of the JJEM that imparts a natal kick to the NS, the kick-by-early asymmetrical pair (kick-BEAP) mechanism. At the early phase of the explosion process, the NS launches a pair of jets where one jet is much more energetic than the counter jet. The more energetic jet compresses a dense side to the CCSNR,and,by momentum conservation,the NS recoils in the opposite direction. Our study supports the JJEM as the primary explosion mechanism of core-collapse supernovae and enriches this explosion mechanism by introducing the novel kick-BEAP mechanism.