The word आस्तिक comes from the verbal root अस् meaning “to exist, to be” — आस्तिक meaning “one who believes”
Logically, नास्तिक means “one who doesn’t believe”
Believe in what, you ask?
श्रुतिस्तु वेदो विज्ञेयो (That which is heard is recognized as the veda)
धर्मशास्त्रं तु वै स्मृतिः (Verily then the recollection (smRti) are the dharmashastra)