A good case against God

[Skepsis]

I assume then you have no good argument or verbalizable reason to think that they are true. It seems to me that you know them by intuition or experience, the same way many people know God exists.

No, it is called foundationalism. Look it up. They are necessary presuppositions to function in the world. The reason you make them is to avoid killing yourself or mental illness. All famous nihilists were radical skeptics and generally died in strange suicide. One even hung himself in his insane asylum with a sock after writing a series of letters signed "Jesus Christ".
These presupposions aren't known by intuition, they are understood by sense perception and validated by necessity. Surely you can't be so dense as to equate this to God(s).

God's existence is falsifiable. People in the past have thought they falsified it by using the problem of evil or finding an incoherence in the attributes of God. However, I think such attempts have failed. As for being immaterial etc… I would remind you that these are not ad-hoc properties of God as the result of modern science, they have been around long before that.

God has no ad hoc properties. It is just a being that is revered and seen to be the "greatest" of something. As it stands, you still haven't properly defined God, so I have nothing to work with. Also, I can present the argument from evil in a way that isn't possible to refute. I generally don't use it as it only means that, if there is a God, he is a prick. I don't like granting God's existence even for the sake of argument because sometimes the idiots I'm arguing against take it the wrong way and say something like, "Oh, so I see you are suppressing God..."
Be sure to define your God, so I can eliminate your proposition.
Oh, and to adress you specifically, he is practically unfalsifialbe. Unless you say that he interacts with the world or has any traits that might have influenced creation, then he is unfalsifiable and thus an unresticted negative proposal.

Does it follow that you should also believe that there are no extra-terrestrials in the universe? I don't think so. I also do not accept that there is no evidence, I just think that the evidence is experiential and intuitive rather than demonstrable.

Here we are. I found the stumbling block that you are struggling to get past with all your intellectual prowess, but you are failing miserably.
So here it is:
You cannot or will not distinguish between lack of belief and belief in the inverse/belief that proposition x is untrue. Like Cthulu Dreaming has said a number of times, you need to understand the difference between
I believe in the existence of x and
I believe the existence of x is likely.

I believe that the existence of aliens that have visited Earth to be immensely unlikely. I believe the existence of extraterrestrial low-level life forms to be very likely.

It doesn't follow that you should "believe there are no aliens in the universe", but it does follow that you shouldn't believe there are aliens.

It comes down to this simple breakdown: You either
1. Believe there are no- x(s) -in existence
2. Believe there are- x(s) -in existence
3. Don't believe there to be any- x(s) -in existence.

Hopefully I shed some light on the topic.