Positronium in the $2^3S$ metastable state exhibits a low electrical polarizability and a long lifetime (1140 ns) making it a promising candidate for interferometry experiments with a neutral matter-antimatter system. In the present work, $2^3S$ positronium is produced - in absence of electric field - via spontaneous radiative decay from the $3^3P$ level populated with a 205nm UV laser pulse. Thanks to the short temporal length of the pulse, 1.5 ns full-width at half maximum, different velocity populations of a positronium cloud emitted from a nanochannelled positron/positronium converter were selected by delaying the excitation pulse with respect to the production instant. $ 2^3S $ positronium atoms with velocity tuned between $ 7 cdot 10^4 $ m/s and $ 10 cdot 10^4 $ m/s were thus produced. Depending on the selected velocity, a $2^3S$ production effciency ranging from $sim 0.8 %$ to $sim 1.7%$, with respect to the total amount of emitted positronium, was obtained. The observed results give a branching ratio for the $3^3P$-$2^3S$ spontaneous decay of $(9.7 pm 2.7) % $. The present velocity selection technique could allow to produce an almost monochromatic beam of $sim 1 cdot 10^3 $ $2^3S$ atoms with a velocity spread $ < 10^4 $ m/s and an angular divergence of $sim$ 50 mrad.
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