Use playsound command like this:
/playsound minecraft:block.wood_pressureplate.click_on @p
It plays the sound like the one that clicks the GUI button in minecraft instead of the one that step on the wooden pressure plate, but if the sound subtitle shows, they look the same in subtitle.
Same issue when playing sound: "block.tripwire.click_on".
You have to change the pitch. The game uses a pitch of 0.8 for wooden pressure plates: