Yes.
The universe has been going for at least 13.5 billion years.
If I say I've lived in my house for 10 years, does that mean the house never existed before I moved in? No - all it means is that the house is at least 10 years old. It could be older and have had prior occupants, or it could indeed have been made 10 years ago. The evidence is insufficient to decide either way.
I'm not one to disagree with you very often but, based on books and textbooks I've read, it seems that its commonly accepted in the scientific community that the universe began as a singularity which then "became" the Big Bang which has led to the expansion as we observe it.
"The Big Bang was the
event which led to the
formation of the universe, according to the prevailing cosmological theory of the universe's early development (known as the Big Bang theory or Big Bang model). According to the Big Bang model, the universe, originally in an extremely hot and dense state that expanded rapidly, has since cooled by expanding to the present diluted state, and continues to expand today" -good ol' Wikipedia (emphasis mine).
It seems most physicists would say that the universe "began" 13.5 billion in the Big Bang rather than them saying the universe is expanding currently via the "process" of the Big Bang. The Big Bang, however accidental a term, seems to imply an event, not a process.
I have many problems with this theory, as well as the notion of an expanding universe. Its not really based on evidence, it just based on my own thought experiments (like the "Strange Idea" which you replied to). For example, here's another one:
Lets say at T=0 you have a quasar which forms. This quasar starts emitting light.
Now, you have T=12 billion years. The light from this quasar now reaches Earth, and the light from the quasar is 12 billion years old.
But at T=12 billion years, where is the quasar and how far away is it from the Earth? Because the quasar formed at T=0, which was supposedly 12 billion years ago. So the light we see on Earth is light from T=0, not T=12 billion.
This seems to imply that, at T=12 billion, the quasar, (if it still exists, and if the universe is expanding) is much further from Earth now. But it cannot be further than 12 billion years away because that would contradict the notion of it moving faster than the speed of light.
It makes my head hurt, but I feel like there's a contradiction hiding in there somewhere.