Many atheists are inclined to argue that the only purpose we have is that which we create for ourselves. But creating a purpose qualifies as a purpose in and of itself. IOW, whatever is driving the atheist to create a purpose is itself a purpose which the atheist him- or herself did not create.
Question: Is it possible for us to create a purpose without acting on some higher purpose (which we ourselves did not create)?
"The good is what all desire." - St. Thomas Aquinas
"Purpose" is not quite the same idea as "intention." What we intend is the result of design: we anticipate, predict, and then manipulate to construct things or make things happen. Intention is not a force but a recognition that we should play a part in resolving a need. We could also choose to abstain.
A purpose, on the other hand, is assigned. In the above example, we might find purpose in the role we can play to resolve a need. Purpose or reason is a type of explanation intended to make sense of the willful or active role in the outcome.
It is entirely a simple thing (and, yes, possible) for us to assign purpose to any part of a description of activity. It possibly has to do with latent beliefs in animism, but in any case the act comes first and then the purpose.