Using textit{in situ} polarized neutron reflectometry, the depth resolved evolution of the magnetism and structure in a Pd/Fe/Pd trilayer thin-film is measured during growth. The initial film structure of Pd/Fe shows a small proximity induced magnetism in the underlayer and a magnetization in the Fe layer of $approx1.6$,$mu_{text{B}}$ per Fe atom, less than the expected bulk value of $2.2$,$mu_{text{B}}$. Deposition of the Pd capping layer initially follows an island-like growth mode with subsequent coalescence. With increasing Pd deposition the Fe moment and the proximity-induced magnetism in the Pd capping layer decrease. After final deposition of the Pd capping layer, the magnetic profile is structurally and magnetically symmetric across the Fe layer, with magnetism induced in Pd up to 0.92 ,nm from the interface. Throughout the Pd deposition the Pd/Fe/Pd trilayer structure is becoming increasingly symmetric, a fact which points to a Dzyaloshinskii-Moriya interaction as a likely cause of the observed magnetic behavior.