We address the kinetic competition between charge striped order and superconductivity in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_{4}$. Ultrafast optical excitation is tuned to a mid-infrared 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 $T_{CO} approx$ 80 K, far above the equilibrium superconducting transition temperature of any lanthanide cuprate. Two key observations are extracted from the relaxation kinetics of the interlayer coupling. Firstly, the plasma mode relaxes through a collapse of its coherence length and not its density. Secondly, two distinct kinetic regimes are observed for this relaxation, above and below spin order transition $T_{SO} =$ 25 K. Especially, the temperature independent relaxation rate observed below $T_{SO}$ 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 tunnelling by disruptive interference rather than by depleting the condensate.
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