While there are some exceptions, physics generally holds that the universe has a beginning.
Assuming that there is a first cause of the universe, what are the logical based reasons for preferring either simple/unintelligent first cause or a complex/intelligent first cause?
Nothing versus something
If nothing caused the Big Bang, then the Big Bang was not caused by anything, it just happened. Or how could nothingness cause somethingness? How could an empty function on zero, return any number other than zero?
Simple versus complex
There is a tendency to suppose that simple inputs, when coupled with sufficiently complex functions, yield progressively complex outputs. The functions in question, here, would be the laws of physics; the inputs, the state of matter/energy (such as it was) "in the beginning." We seem unable to avoid having either the matter or the form of physics, be relatively complex, in order to yield a complex enough later cosmos; though the preference is to attribute the complexity to the form, rather than to the matter.
Unintelligent versus intelligent
I stayed at a homeless shelter in Salt Lake City for almost a year, and we often had a creationist preacher come by for nightly chapel services. He thought it was silly to think that the materials used to construct large buildings might just fly together by happenstance, into the shape of a building. I concurred, technically, but I was also aware that carbon, which is one of the key chemical bases of known life, has a reliable capacity to form complex structures according to otherwise "unintelligent" quasi-geometrical principles. As far as I know, no state of affairs that obtains in the modern universe, clearly absolutely requires a primordial intellect to explain (though some require non-primordial intellects, e.g. facts about human-produced artifacts).
'Has a beginning' is problematic if time started there. What does 'before time' mean?
We know reconciling relativistic spacetime with the quantum picture is the biggest challenge in physics - explaining time in terms of something else.
As discussed here we either look to a higher dimensional space like brane space or the E8 octonion hyperstructure, or some kind of monism with dimensions as emergent symmetries: How can time have a beginning when a beginning needs time? This latter could fit say with conformal cyclic cosmology, where complexity & structure emerged through repeated cycles from a foundation of the uncertainty principle.
Causation is deeply suspect, as Hume pointed out what we really have are regularities. Causation seems to be part of a cognitive bias towards narratives, as discussed here: Is the idea of a causal chain physical (or even scientific)?
This type of question represents a very active area of mathematical physics research. Great volumes have been written about it but they all require a lot of mathematical training to understand because the problem is extremely complex. As such, philosophy has nothing useful to contribute to the field.
It is also worth noting that if we run time backwards and track the universe right back to when we know it began, there comes a point in the exercise where the conditions in the very, very early universe become so extreme that all our mathematical models of what's happening up to that point are known to break down. Earlier than that (we're talking just millionths of a second after the Big Bang!) we have no useful theories to guide the model building and no one can say what was going on there.
One of the very few useful books written for nonphysicists on this topic is The First Three Minutes by Stephen Weinberg. I highly recommend it.
