Having a No Pass in major class for a reason
If you do excellent work for the rest of your undergraduate career, consistent
with standards required for graduate school, I doubt that anyone will notice
one NP on the record in your freshman year. 

Ideally, one of the professors writing a letter of recommendation 3.5 years from now can make
the briefest of mentions of an 'administrative snafu' at the start being
the only blemish on an excellent transcript. Especially in that case, you can get by
without making a fuss over it in your letter of application. (In any case, I'm not sure you should draw attention to it.)

Two or three years from now, If this still seems an issue for you, you might investigate
whether there is some sort of retroactive withdrawal procedure. With a couple
of years of solid work in the department, you may have more leverage 
for a successful investigation. Also, your current department has a stake in 
establishing a record of 'getting its best students into' first-rate
graduate programs. 

To be sure, there are mistakes one can make that unfairly foreclose future
options. But I would be very much surprised if this is one of them.