Yes there are many possibilities. Some are already in the domain of respected science... eg Steady State universe.
"Big Bang" was coined by Fred Hoyle. The term had wide appeal to creationists and ever since then many scientists have been trying to make the suit fit.
There is no reason to believe the universe is not infinite and filled infinitely with galaxies and stars and planets except the boneheads who keep trying to prove Big Bang is a legitimate answer.
But Big Bang suffers the same problem as the God concept. What came before? What lies outside of the known universe?
In my opinion Big Bang theory is for idiots. I said it, I mean it.