Not all events necessarily have causes
- everything that exists must have a cause or,
- everything that begins to exist has a cause.
These statements are arguably a hasty generalization from a limited set of observations. Scientific consensus for a clockwork deterministic universe was mainstream in classical physics until the end of the 19th century. With the discovery of radioactivity and quantum mechanics in the 20th century, the issue of causality in physics has become much more ambiguous and determinism is generally rejected.
This argument does not claim certain knowledge that some event do not have causes, which would be difficult to establish scientifically. All that is required is to establish the possibility of uncaused events.
There's nothing in the laws of physics which demands that the law of cause and effect be more than generalizations for interacting with the world above the quantum level. This undermines the premise that "Everything that begins to exist has a cause."
The technical name for the concept is the Glendower problem. The opposite view is the principle of sufficient reason. A similar concept is a "brute fact", which is a fact which is true but does not have an explanation or rely on any other fact.
Radioactivity and quantum mechanics
There is no known way to predict the timing of the radioactive decay of single atom e.g. from isotope Carbon-14 to Carbon-12.
- "Radioactive decay is determined by quantum mechanics – which is inherently probabilistic. So it’s impossible to work out when any particular atom will decay, but we can make predictions based on the statistical behaviour of large numbers of atoms. "
Virtual particles are short lived but very real particles (usually pairs?) that come into existence and then annihilate each other. It is possible that the formation of virtual particles do not have a specific cause, since they occur in a vacuum, but are statistically random. Virtual particles exist for such short times that they cannot be directly observed. They can be observed indirectly by the Casimir effect. 
- "Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways. These predictions are very well understood and tested. "
Further, similar quantum considerations could have direct analogies to the Big Bang which might be causeless. The universe was very small in the first fraction of a second after the Big Bang and quantum effects were very significant.
Unknown uncaused physical phenomena
The formation of space-time and what, if anything, came before is poorly understood. Time may have come into existence at the Big Bang.
There may have been unknown processes that operated in the early in the universe or prior to the Big Bang. These may have been without cause. Thunderf00t's video on Kalam questions the validity of using everyday concepts like "everything that begins to exist has a cause" in extreme situations such as the beginning of the universe.  Hume argues the only way to know if principles (such as causality) hold in very different conditions is to have direct experience of it:
- "Is nature in one situation, a certain rule for nature in another situation vastly different from the former?"
Philosophy of causality
Presumably people have always raised causal arguments, but the philosophical analysis of causality essentially begins with Aristotle (384-322 BCE). Aristotle’s causal theory is too extensive and complicated to be worth describing here, but it is enough to mention that it is founded on exploring the different ways one can answer the question “why?” (as in “Why was this brick building built?”). Many philosophers continue to our day to proceed in similar analysis of the concept of causality and characteristics of satisfying answers, but this is not what we are looking for - we are looking for an argument for why we should hold a particular causal principle. Most of the philosophical treatment of causality is therefore irrelevant, and we will not cover it.
The justification of causality can be divided to before and after David Hume (1711-1776). Before Hume it was taken for granted that causal laws, like (1a), existed, and we could derive them from reason and experience. David Hume pointed out that there is no way to derive a causality principle from pure reason, as there is no self-contradiction in it failing to hold. On the other hand, in fact we never see the causal connection itself, only the regularity of events. We see that we push an object and that it moves, but we don’t actually see that the push is the cause of the movement. By inductive reasoning, we can conjecture that it is the cause, but we will always remain with the theoretical possibility that we were wrong, that one day we will push and the object will not move. There is, therefore, no philosophical justification for any causality principle at all - only a scientific one. This conclusion of Hume still holds, despite the attempts of substantive opponents to undermine it.
The most significant attempt to provide a philosophical justification for a causal principle was given by Immanuel Kant (1724-1804). Kant effectively claimed that the structure of human consciousness compels us to see the world through “glasses” of cause and effect, so we impose a description in terms of cause and effect onto the world. But this explanation does not suffice. It is true, as Kant maintained, that Reason is only possible if one can apply the categories of cause and effect (for otherwise one cannot think, make plans, learn from experience, and so on) - but this shows only that reason is not prior to causality, that it is possible only given sufficient causality (causality applying to its own workings and its relations to the world). This does not imply that causality applies to all physical states of affairs (as we will see below, it doesn’t).
Quantum mechanics says that certain things are impossible to predict (by the uncertainty principle) but this is distinct from not having a cause at all. The causes may originate in higher dimensions that we cannot directly observe.
- "I don't understand your misgivings about my response to the claim that virtual particles are uncaused. They're not. They are fluctuations of the energy in the vacuum. The quantum vacuum is not nothing. "
However, the point is the timing of the event cannot be predicted yet and is potentially causeless. Saying they occur in a medium, in this case the quantum vacuum, is not relevant since the media does not explain the timing of the occurrence. Given current scientific understanding, it is difficult to say if some quantum events have a cause or not. This counter-argument still does not establish the argument premise with certainty.
Self creating objects violates the conservation of energy
- If God exists, the universe is an open system.
- Without God, the universe as a closed system.
- The First Law of Thermodynamics states that in a closed system, the amount of energy present in that system is constant.
- So, if the Universe as a whole initially contained no mass/matter/energy (energy input is equal to zero)
- Then we would not see the currently observed universe
- Therefore the universe is not closed and therefore is open.
- Therefore God exists.
A few problems with this:
- The universe could have self-created with the mass and energy already present.
- The universe can be an open system in a multiverse without God.
- The universe could have existed forever. (see original counter-argument: Second law of thermodynamics implies the universe is of finite age)
- If energy is conserved, where did God get it from.
- If God can create energy, why cannot a natural process?
- No particular God is implied
- The universe could be closed, have zero total energy and still match the observed universe! This theory is called the zero-energy universe. 
Virtual particles can briefly exist in apparent violation of the conservation of energy.  Perhaps objects can exist for longer periods in certain circumstances.
- Radioactivity, Institute of Physics, retrieved 13 Apr 2014 
- Why do people laugh at creationists? (part 37) William Lane Craig: Thunderf00t's video on Lane Craig's version of the Kalam Cosmological Argument
- William Lane Craig, Objections to the Causal Principle, Q&A #117 
- Jeff Miller, God and the Laws of Thermodynamics: A Mechanical Engineer’s Perspective, 2007 
- Zero-energy universe on wikipedia