What has convinced you

There is only One Truth. That Truth is God.

Epignosis exposes gnosis.

If I understand what you are saying it amounts to "it is what it is" which isn't really saying anything. The statement "some reality exists" tells us literally nothing about that reality. If that is all you can know then all of your claims about reality other than that it exists at all can be dismissed which rather undercuts any value you might have as a teacher. Why do you claim to have things to teach people if literally the only thing that can be known is an obviously apparent tautology?

If it is not The Ultimate Reality, it is ultimately unreal.

We can only know God through unreality. If that wasn't the case, God wouldn't be what God is.

The Truth is greater than knowledge.

How does one come to know anything reliably through unreality? Unless you can explain this I have no choice but to consider it nonsense. If all one can know is unreality then one can know nothing. Under such circumstances one cannot even know when one farts.

Put your faith in God, not on your own understanding. That is true knowledge.

Faith can lead equally to contradictory beliefs. I could as easily believe in Vishnu, Allah, Yahweh or the flying spaghetti monster based on faith. If faith can lead equally to truth and untruth how can we possibly consider faith to be a good pathway to truth?

The Ultimate Reality is The One True God.

Here is a definition of faith you may not be familiar with.. courtesy Merriam-webster...

"something that is believed especially with strong conviction"

Definition of "conviction" courtesy Merriam-webster 

My faith is in The Ultimate Reality. That is monotheism.

Is there anything one cannot believe on Faith?

Faith has been turned into a dirty word by God deniers, but even the God deniers have faith. We all have faith. Faith is a good thing.

Can you believe anything without faith? I say no. There is always faith involved, conscious or not. Even going against your faith requires faith.

That is not what I asked. Allow me to restate my question for your convenience.

Is there any position that cannot be held based on faith?

It´s just faith to be honest. I don´t really have much of a justification. I couldn´t tell you that I´m completely convinced nor am I totally observant, but here we go: 

I think that if God is all powerful than he knows more than we do, so questioning him via human logic is essentially pointless. 

I do however think that the illogical nature of belief could work with the Tanakh, being that it is reliant on Faith and your individuality and ability to choose as a human. I think it makes sense in this context because being able to have Faith despite a logical argument against God demonstrates that your Faith is strong. 

I am pretty confident that believing is the right way, but me as well as many other Conservative Jews would testify that as long as you are a good person, you´re pretty much golden no matter what. 

As I did answer...

No.

Faith doesn't have to be based on strong conviction.

But in my case it certainly is.

I'm not sure you understand my question.

Perhaps if I reword it.

Is it possible to believe in aliens just because you have faith that they exist?

Of course.

Allow me to be more precise. Is it possible to believe in extraterrestrial life just because you have faith that it exists?

Certainly. Do you believe there was ever a man on the moon? Do you believe that there are people living in space stations above the atmosphere? These are examples of extraterrestrial life.

Definition of extraterrestrial courtesy Merriam-webster 

"originating, existing, or occurring outside the earth or its atmosphere"

If you believe there are astronauts in space, where does this belief come from?

Faith. 

Okay let me be more precise still. Is it possible to believe that there is life outside our solar system just because you have faith there is?

You are wrong for two reasons.

One, you have to have faith that the video footage isn't fabricated like any fictional movie.

Two, evidence you find convincing leads to strong conviction which gives you faith.

You can believe anything on faith, true or false things. But faith in itself is required to believe anything. To disbelieve anything even requires faith. Real faith tends to come from strong conviction, meaning that what the faith is in has been proven fo the one who has faith.

Why do I have faith in God? Because it is impossible for me to doubt at this point. Were their doubts in the past from me? Certainly, but now I am absolutely sure. It was my doubts that lead me to such secure faith. 

Is it possible to believe that there is life outside our solar system just because you have faith there is?

I only believe that astronauts are or have been in space if my perception accurately reflect reality. I do not so much believe as accept as a convenience. I don't have faith I have reasonable expectations based on past experience.

There are people who believe if you vibrate your sacral chakrah at just the right frequency you can crap out perfectly intact chocolate muffins.

They take that on faith.

The point is, when something has been proven to somebody because of evidence, they tend to have stronger faith than the person who simply taking a risk.

If you believe in something because you believe the evidence points to it beimg true you have faith because of strong conviction. If this is hard to believe, it's probably because you've been influenced by atheistic thinking, which if you can't recall, had you professing a position that literally means that there is no truth. Atheist arguments are subversive and contingent on redefining language to make the kind of things I am trying to tell you unintelligible. 

This whole worldview is about drawing you away from God by confusing your language and making you superstitious while getting you to believe you are rejecting superstitious.

So you accept that God means The Ultimate Reality. Think about how you were tricked into denying this, and realize that the deception goes far deeper than that. This is something you are going to have to do on your own. Love the truth, be sincere, and you'll get out of it fine on your own.