Does the Qur’an and/or hadiths address beliefs such as atheism (statements like ‘there is no god’)?
It is being mentioned in the Al-Quran.
Surah Al-Jathiyah, verse 24. (45.24): Reference and link here
Translation: And they say: "There is no life other than our life in this world. We die and we live (alternately); and nothing destroys us except the passage of time". In fact they have no knowledge of it; they are mere conjecture.
Surah al-An’am, verse 29. (6.29): Reference and link here
Translation: They insisted, “There is nothing beyond this worldly life and we will never be resurrected.
Article by Mufti Wilayah Persekutuan Malaysia. Original version in Malay here. English version in Google Translate here.
Tafsir Maarif-ul-Quran. Interpretation of Surah Al-Jathiyah, verse 25. (45:24). Click here to read.
The qur'an mentions both atheism الإلحاد and the corresponding verb ألحد, يلحد (however more in the meaning of reject and refute) in several verses. Note that the modern day/use terminology is not necessarily a 100% match for the meaning of both Arabic terms.
Atheism mentioned in the qur'an
Some of the verses mentioning atheism are (with some comments):
Life is not but our worldly life - we die and live, but we will not be resurrected. (23:37)
This verse is clearly talking about atheism. People saying so reject everything, Allah, Angels, Messengers, Miracles etc., see also (6:29), (45:24). Their thinking is also displayed in:
And he presents for Us an example and forgets his [own] creation. He says, "Who will give life to bones while they are (36:78)
And to Allah belong the best names, so invoke Him by them. And leave [the company of] those who practice deviation concerning His names. They will be recompensed for what they have been doing. (7:180)
These people are rejecting Allah's existence and therefore his names too.
They said, "You are not but human beings like us, and the Most Merciful has not revealed a thing. You are only telling lies." (36:15)
And they will say, "If only we had been listening or reasoning, we would not be among the companions of the Blaze." (67:10)
These two verse show a kind of people who reject the prophecies, messengers and miracles which also is a reference for atheism. Their behavior and thinking was explained also in:
And if they see a miracle, they turn away and say, "Passing magic." (2)
And they denied and followed their inclinations. But for every matter is a [time of] settlement.
Indeed, those who inject deviation into Our verses are not concealed from Us. ...
Is regarded as an example of refusal or rejection of the qur'an and Allah's revelations and therefore as a kind of atheism.
Atheism mentioned in the sunnah
The sunnah also reveals covers the topic of atheism -in the modern day meaning- and some atheistic thoughts here just an example:
Allah's Messenger (ﷺ) said, "Satan comes to one of you and says, 'Who created so-and-so? 'till he says, 'Who has created your Lord?' So, when he inspires such a question, one should seek refuge with Allah and give up such thoughts."
(See for example in Sahih al-Bukhari)