How will those who deny the existence of Allah Almighty be tested, as opposed to the disbelievers who believed in the existence of a god but disbelieved in Islam?

Allah does not punish anyone except after the 'Risali Hujjah' (the conclusive proof brought by the Messenger) has been established against them. This proof is not established against a non-Muslim unless the call of Islam reaches them in a way they can understand. Thus, all types of disbelievers – even atheists – can be considered among 'Ahl al-Fatra' (people of the interregnum, who lived between two prophets) due to the call not reaching them. Scholars have differed regarding the ruling on 'Ahl al-Fatra' in the afterlife, and the most preponderant opinion is that they will be tested therein. Disbelief, by consensus of Muslims, is the absence of faith. And whoever does not believe after the 'Hujjah' has been established against them through the message is a disbeliever, whether they are a denier, a doubter, an averse one, an arrogant one, or a hesitant one.