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Ca₂RuO₄ is a prototypical multi-band Mott insulator, with a metal-insulator transition (MIT) at T_MI = 357 K accompanied by a structural phase transition characterized by a compression of the c axis. We present an angle-resolved photoemission spectroscopy (ARPES) study of the electronic structure evolution across the MIT on a series of La-substituted single crystals Ca_2-xLa_xRuO₄ grown through the floating zone technique. We find that La-substitution does not introduce itinerant carriers in the insulating state, but suppresses the MIT to zero temperature for x > 0.1, permitting a detailed study of the correlated metallic state emerging from the Mott insulating ground state. Our data show that metallicity arises at the structural phase transition after a marked redistribution of spectral weight from the xy orbital, which is completely filled in the Mott state, to the out-of-plane xz/yz bands. The metallic phase has a well-defined Fermi surface of heavy quasiparticle states and shows enhanced signatures of spin-orbit coupling. Dynamical mean field theory calculations are in good agreement with our data and confirm that correlations enhance the bare spin-orbit interaction in ruthenates.