In the past I would agree with you, but thinking about it more carefully, I’m not sure this has to be the case. Reasoning doesn’t have to proceed “from the larger to the smaller” (i.e. from God to the Christian God), even if a philosophical system is more elegant if phrased in that way. Someone who believes in Jesus first (for example by looking at the evidence of the Resurrection) could have the following two prior beliefs before they seriously considered Christianity or theism, just from common sense:
- If someone does X, God exists. (i.e. it is impossible for someone to do X without God being behind it)
- If God exists and Jesus did X, then the Christian account of God is true.
Then after they started seriously reading the Bible, they could start to be convinced of the following:
3. Jesus did X. (where X could be the Resurrection, or preach a certain unique, compelling message)
4. From 1, 3: God exists
5. From 2, 4: Christianity is true.
The difference between such a converted person and a Jew or Muslim would be that the latter rejects proposition 3).
In science, we do this all the time, in that often the truth or falsity of an entire theoretical system depends on a few landmark experiments. Later, in textbooks the material could be represented in a way such that it is derived from “first principles” (e.g. Einstein’s Special Relativity), but neither in practice nor in history does everyone actually think in that way.
Now it seems that there is something to the fact that they are called “first principles” - which is why you could call them “logically prior”. But it seems to me there is nothing that necessitates them being logically prior. The reasoning process I described above follows logical rules and doesn’t seem fundamentally inferior (except for reasons of logical “elegance”) to the one where one is first convinced on independent grounds that “God exists”, before moving on to Jesus.