No. The word ‘atheist’ never needs to be written with a capital letter (except in cases where any word is – such as at the start of a sentence).
Words like ‘Christian’, ‘Jew’, and ‘Buddhist’ are always written with capital letters because they are proper nouns – much like names of countries, cities, or people.
The word ‘atheist’ is not a proper noun – it’s just a regular noun (and an adjective). It does not refer to a member of an organised group or a particular culture or tradition. It simply refers to someone who takes a single philosophical position. The most comparable words to it are words like ‘monotheist’ (someone who believes in a single god) and ‘polytheist’ (someone who believes in multiple gods), neither of which are generally capitalised.
An exception is in the term ‘New Atheist’. New Atheism was a movement that was most popular around 2008-2012, and the people who were part of it are called ‘New Atheists’. Both words of this term are typically capitalised to make it easy to recognise that it refers specifically to a participant of this movement.