Seems I am answering this question a lot lately.
Conventional wisdom says that the distance from the top of the first fret to the bottom of the string should be about .020". Most of the luthiers I know recommend this. I do not.
If I fret my Number One at the second fret and measure the gap at the 3rd fret, I find the gap to be very close to .010". Same if I fret at the first fret and measure at the second. In other words the gap I need at the next fret from where I am fretting is .010", at least in this area of the neck. So that tells me I need a clearance of .010" at the first fret when "fretting" in the zero fret position a.k.a. the nut. If .010" is enough clearance over the second fret, it's enough over the first, and that will occur when the nut is set to provide .010" of clearance there. It may be advisable to add a couple of thousandths of an inch to account for wear over time, but anything beyond that serves no purpose.
So you can use the tap test by depressing the string between the 2nd and third frets so that it it touching the second fret. If there is a gap between the first fret and the string you will hear it by very lightly tapping the string directly above the first fret and listening for a "click". No click indicates that the string is too far from the fret or it's already resting on it. In either case the nut slot is not right. If you do get a tiny click, then it's in the ballpark. That may be good enough, depending on how fussy you are.