My arguments in favor deism will probably annoy a few folks, because it requires twisting your mind a bit to think about some odd concepts.
To start with:
Do you believe in acausality? Acausality means getting something from nothing. Many physicists believe in acausality. Specifically, they believe that reality has a time where T=0. This is a starting point where time began. To them, there is nothing before this moment. Thus, they believe that reality, at its starting point, just came into existence without a cause.
I find the idea of acausality to be fundamentally counterintuitive. I feel that it is just a belief in magic. "It just is" is never a good answer. Better to say "I don't know" and leave it at that, than to lower oneself to magic-like thinking.
If you reject acausality, it changes everything. Causality cannot occur without some sort of time. Time, as we experience it, is a component of space-time. Space-time is the medium in which our reality is defined. That is, particles and waves are defined by patterns of resonance within space-time. Well, that is a bastardized version of what many physicists believe, anyway.
So, the fundamental problem here is that time is necessary for causality. And yet time, as we experience it, began with the big bang. This does not mean there was not time before the big bang, this just means that our time, as a component of space-time, did not exist before the big bang. Thus, there had to be some other sort of time. This leads to the concept of multiple dimensions of time.
This is not too difficult to comprehend. Think of an excel spreadsheet, with 12 columns, where each column represents a month. In this example, the formulas for the cells are set up so that you enter information into the first column, and all of the data for the subsequent columns is filled in automatically - calculated be formulas.
The data in this spreadsheet can be thought of as a miniature reality. The spreadsheet is the fabric of space-time. Time began at the first month. For any given month, you can ask, "what caused things to be this way" and the answer will be "the way things were in the previous month." This is fine for all months except the first month. For the first month there is no previous month to cite as a cause. Instead, the cause lies outside of the space-time of that reality.
In this setup, you have two dimensions of space-time. The inner dimension would be the months that are a component of the spreadsheet. The outer dimension of time would be the flow of events that you experience, which included creating the spreadsheet and entering data into column 1.
If you reject acausality, and believe that time in our reality had a starting point, then you have to conclude that the cause of our reality lies outside of our reality. This would imply the existence of a greater reality, of which our reality is a subset.
There are other arguments in favor of this type of "multiverse" idea. So called "spooky action at a distance" - which is a phenomenon found in physics - seems to indicate faster-than-light causality. It does not permit the transmission of a signal, and thus cannot be used for faster-than-light communication, but it does indicate some mechanism of action that lies outside of our light-speed-limited space-time.
If our reality is part of a multiverse, this changes everything.
For this purpose, I define a god as a being that has the power to design and implement a reality, such as the one we live in.
If the outermost dimension of time goes back forever, and the probability of a god evolving into existence is greater than zero, then, given forever, such a being would eventually evolve into existence.
In other words, if it is at all possible for such a being to exist, then given enough time, such a being would come into existence one way or another.
This means the probability of at least one god existing is very high - in fact, the probability approaches 100% (but this is only true if it is possible for such a being to exist).
So, is it possible for a god to exist? Given that the outermost reality has given birth to an entire universe (ours) and one would imagine other universes as well - the evolution of a superbeing of great power does not seem unlikely.
This leads to a rather difficult concept - when did god(s) evolve into existence? No matter where you are in the outermost dimension of time, the amount of time that precedes you is infinite. Thus, the moment at which god(s) came into existence would always lie in the past. Is this the same as having always existed? I don't know, but it is close.
The fining-tuning argument is based on the idea that the constants of nature look an awful lot like they were designed for emergence - that is, designed for life to be possible. If we believe that a designer(s) exists, then that lends considerable weight to the idea that our reality was designed, rather than happened by accident.
I have much more to say on this concept, but this should be a good start for now.