Firstly, the idea that consciousness is primarily physical is backed up quite heavily within neuroscience. Brain injuries can cause distinct shifts in how our personalities work.
If a scientist already believes there is only physical existence, this can effect how the person interprets things. And our character has a lot to do with what we want to believe; we can want certain things to be true, and so we see things that way, using whatever is put before us.
So . . . if a person becomes brain damaged, the person can adapt to the change, so that the person shows a different personality; but that different way of expressing will be connected to the person's real, deep-down character.
For another possible example > a person might act very nice, but then get Alzheimer's. As the person's memory changes, the person might forget to put on that show of being nice, and then can start acting out, showing how all along the person was deeply nasty. Or a nasty controlling person might change to forget what the person was so nasty about, and then act sweet because the workers charm him or her.
But the character of wanting his or her own way is still there.
I now am gnawing on some turkey bones, by the way, while thinking and writing about this. So, in case you do think I'm a real turkey to think like this, may be it's the turkey bones. If you believe the physical can effect our personalities and how we see things . . . possibly you could believe that my chewing at turkey bones can effect my thinking

But even though my personality might show differently while I am chewing at turkey bones, I am still me, deeper.
Well, the bones might distract me, so my thinking is different than if I were not gnawing bird bones; and so I could seem like I am a bird-brain while relating with these bones. My personality might show differently while I am enjoying some meaty bones, but this does not mean I have changed to a different personality, necessarily > personalities can have different moods and manners of giving attention, at different times; it can have a lot to do with who and what is getting their attention.
Preference for pleasure can have a lot to do with how a personality shows. If a person is brain damaged, the personality can develop in relation to how now the person now can not get certain pleasures or have the control that the person wants. The person can get nasty or depressed . . . or say, ok now I can rest more - - depending on how the person is, deeper than the shown personality.
The study of split-brain patients is particularly interesting; apparently cutting the corpus callosum in half (this is done to alleviate seizures) essentially creates two distinct, different personalities. Did splitting the brain somehow create two souls?
Each side of the brain is capable of different things; so it can be the same person developing emotionally in relation to what each side is able to do, and how each side is functioning.
I suppose, too, that there can be memory stored, different on each side. So, the person may be acting according to each h side's memory. But deeper is the real person, with that person's character having a lot to do with what the person does.
Especially interesting for people who believe in hell is the case where one personality is a theist and one is not.
Even if a person has no brain damage or split brain, still a person can be what the Bible calls
"double-minded" (James 1:5-8). Possibly, this is someone who is capable of, at one moment, believing in God and then, later, not believing in Him. So, a split head could be a way for such a person to express both ways, at once.
And, "of course", there are theists who do not believe in the God of the Bible. So, their character can be similar to that of a non-theist, and therefore capable of showing either a theist personality or a non-theist personality. For one example, a terrorist can be a theist, but act like a sociopath > the same person at one time can show a very religious and family personality, then show a butchering personality.
So, this brings us to your question about faith.
Faith is not only a belief that we can change when it suits our purpose. But plenty of religious people, even, will live their own lives, then all of a sudden have "faith" when they get stuck or want something they have not been able to get; and then can be when they use "faith" to try to get God's attention.
I understand that Biblical faith is
"faith working through love" as Paul says in Galatians 5:6. And
"love", here, means God's own love which He is sharing with us,
"in our hearts", as Paul says in Romans 5:5. So, Christian faith has us in connection with God Himself in us. And our connection with God is our
"evidence of things not seen" which you referred us to, in Hebrews 11:1. We do not see Him . . . physically . . . but in us He is our Proof that He is and how He is in love.
It says faith works
"through love". So, faith is not only thinking something in your head. But I see how faith is our connection with God and His love so we have the effect of God's love on our character > 1 John 4:17. And with Him we have His leading and guiding, in connection with Him >
"But he who is joined to the Lord is one spirit with Him." (1 Corinthians 6:17)