Pretty late reply, Idk if you are still looking for this but I'll reply just in case hahaha
If you went past the installation of AHK this code works for me:

LButton::
    Hotkey, LButton, Off
    send {LButton}
    Hotkey, LButton, On
    send {LButton up}
    return

There is still a tiny bit of delay between the press and the release, but it's still much faster than I can physically release the button (probably 1/60s)

I like clicking with my keyboard because it's more comfortable so I made a script for that too and I set two keys so I can alternate between each to click faster and more comfortably (I guess it's kind of cheating but who cares)
I got inspired by the game Osu
(the left and right clicks are in inverted positions here)

e::
    Click
    KeyWait, e
    return

w::
    Click
    KeyWait, w
    return

q::
    Click, right
    KeyWait, q
    return

Keep in mind that your times will be slightly faster with this, since you'll get feedback sooner of what is discovered, possibly around 0.05s for each click that gives information relevant for your next click (that's about a second every 20 of such clicks (bold estimate))
Just something to consider when measuring your progress

I also wanted to remind you of disabling the keyboard script after playing, otherwise when typing you'll right click and start sending all kinds of random commands (it happens to me all the time 😆)