We address the kinetic competition between charge striped order and superconductivity in La1.675Eu0.2Sr0.125CuO4. Ultrafast optical excitation is tuned to a midinfrared vibrational resonance that destroys charge order and promptly establishes transient coherent interlayer coupling in this material. This effect is evidenced by the appearance of a longitudinal plasma mode reminiscent of a Josephson plasma resonance. We find that coherent interlayer coupling can be generated up to the charge-order transition TCO≈80K, far above the equilibrium superconducting transition temperature of any single layer cuprate. Two key observations are extracted from the relaxation kinetics of the interlayer coupling. First, the plasma mode relaxes through a collapse of its coherence length and not its density. Second, two distinct kinetic regimes are observed for this relaxation, above and below spin-order transition TSO≈25K. In particular, the temperature-independent relaxation rate observed below TSO is anomalous and suggests coexistence of superconductivity and stripes rather than competition. Both observations support arguments that a low temperature coherent stripe (or pair density wave) phase suppresses c-axis tunneling by disruptive interference rather than by depleting the condensate.