Charvaka is the ancient atheist "religion" of India.

Charvakas beleived only in pratyaxa pramANa, or direct perception. ---(1)
Charvakas did not accept inference as an evidence.---(2)

The first question raised against this system is:

Is there any pratyaxa pramANA for axiom 1?
No, there is none, and axiom 1 is an inference, leading to an apa siddhAnta or an internally inconsistant system.

Modern day atheists accept inference and many other sources of knowledge, so this logic no longer holds water against atheism.