The relationship between the cuprate pseudogap (Δ_p) and superconducting gap (Δ_s) remains an unsolved mystery. Here, we present a temperature- and doping-dependent tunneling study of submicron Bi₂Sr₂CaCu₂O_8+δ intrinsic Josephson junctions, which provides a clear evidence that Δ_s closes at a temperature T_c0 well above the superconducting transition temperature T_c but far below the pseudogap opening temperature T*. We show that the superconducting pairing first occurs predominantly on a limited Fermi surface near the node below T_c0, accompanied by a Fermi arc due to the lifetime effects of quasiparticles and Cooper pairs. The arc length has a linear temperature dependence, and as temperature decreases below T_c it reduces to zero while pairing spreads to the antinodal region of the pseudogap leading to a d-wave superconducting gap on the entire Fermi surface at lower temperatures.

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