All beliefs are predicated upon faith, not just religious ones.
This sounds like an attempt to bring other propositions down a level or 5.
You first need to believe that you exist in order to have any following beliefs.
If I don't exist then why do you care, or why would I care? Believing oneself to not exist seems a rather silly thing to do. Even if I am the imaginings of some other being, these imaginings have enough awareness to recognize themself (or rather myself).
Then you need to believe that observation is able to determine facts, if you don't then the previous observation cannot be proven.
While I might be confused (or even delusional) in my own observations, I can consult with others to see if they agree with my observation (that rock is large, the sky is coudy, etc.)
Both of these beliefs are taken upon faith because they're unable to be justified yet predicate all belief.
Again, bringing things down to the level of "faith".
Regardless, if this line of thinking doesn't work then take your own dogma of Naturalism;
Naturalism isn't really a "dogma", but rather a conclusion. It's a conclusion that we all reach at least partially and instinctively. It is nothing more than the realization that the world around us has repeatable properties. We rely on it everyday, all day. If not we would not function. Think just of the process of walking. To walk you must extend one leg in front of you and push with the other, plant your forward foot and then switch them. It is not a matter of faith to understand walking, but an understanding of the regularity of the operations of you legs, the firmness of the ground, etc. that allows you to walk. When the surface rises in front of you, you know you have to lift your leg. When it drops out, as in a step, you know you must ease your forward foot down and you can not just step out on a stop (or from a ledge) as if their is solid, level ground in front of you. We all learn how to do this when we learn to walk and acquire an understanding of the naturalistic nature of walking. Faith will not make your leg move forward, or provide support when going down a stop or off a ledge.
on what basis do you claim that existence (including your own) can be explained through natural phenomena without it being entirely circular and/or assumed?
No system of reasoning is free of at least one or two "basal assumptions", but that does not make it "faith". All naturalistic explanations require is that:
1. There is a naturalistic basis for things
2. It can be discovered.
And these two properties can both be discovered themselves by making the observations and cross-checking them with others and finding the repeat behaviors and patterns. Finding them demonstrates that they exist, and that they can be discovered. Then you work to build upon them and see how much can be so explained. (Answer: virtually everything)
Edit: Even if this fails then do you not take your beliefs on what experts say about reality on faith? You don't know what an astrophysicist, doctor or biologist says is true nor do you even know why what they say is true. The basis for the claims you believe about reality are taken and believed in entirely upon faith.
Ah, but I *do* know what their "beliefs" are and how they know what we know, because I *do* have that training and knowledge.