I would wait, simply until you allow at least one mushroom to become fully mature, as the spawn looks rather like whisps of smoke, released from beneath the fully expanded cap, by the gills below, prior to drying up..
Place a fully grown cap with the mature gills facing downward on a plate, cleaned as well as possible & dried, to collect the 'spore print'.
Otherwise, if you were to damage the mycelium network, you may disrupt the growing cycle. Isn't that why they harvest, by cutting them at the base, as opposed to pulling them up & then removing the base, afterward?
I think I may have once re-used, a Shiitake inoculated, tree log, ( that required banging it hard, to resemble falling to the ground, in the forest, to begin production.) simply by placing a Portabello cap on top... (I stood the log, upright, in a large saucer, to keep it moisture level; ample)
There is an Italian supplier (Bavicchi?) that I used for Pioppino, that was available within the U.S quite inexpensively ( use search terms Italian Seeds + mushroom spawn, or spores) if in case it is the other Italian Seed source, here in the States, if you'd like to try those, with growing instructions...

Yes, they are from that seed brand co., through Italian seed and tool . They offer 5 varieties of edible mushroom spawn at $12.95,including the regular 'white button' kind, plus shipping, with the instructions located at the top of the online page, to place an order.