Maybe!
It depends, though if you mean the Universe as 'the everything' or the physical universe (little u) we find ourselves in and may be part of a greater whole. It also depends whether you mean the Universe as it has turned out to be, or the underlying state of existence which may or may not give rise to a Universe.
The problem is that time is part of the universe (little u), and our normal sense of cause/effect, beginning/end depends on this time already existing. Thus we have to think of any causation in a non-temporal way, possibly from a different dimensional perspective that still allows sequences.
Because of this sequence issue, your 1-3 steps are invalid outwith any sequential dimension. Such a sequential state may or may not be part of the underlying nature of existence, so these steps presume conditions that may be invalid.
On the quantum level, 1-3 is incorrect as things pop into existence and disappear all the time. Virtual particles. At this level, existence is probabilistic, not deterministic, so such sequences are invalid. If any causation of the universe originates at the quantum level, cause & effect need not apply.
It's valid to ask why have we such quantum 'rules' of existence, but we don't know the answer to that as yet as we have no theory of existence. At present it's a very difficult area to research - that's why we build accelerators like the LHC to edge our knowledge forward.
The best descriptions of universe explanations I've encountered so far, and still readable by non-physicists (with a bit of maths) are:
http://sites.google.com/site/alexisbrookex/the-origin-of-the-universe
http://www.infidels.org/library/modern/quentin_smith/self-caused.html
http://www.brighthub.com/science/space/articles/56742.aspx
Also the BA here (not mine!):
https://answersrip.com/question/index?qid=20100708185141AAOCew9