There is no logical requirement of a time before the big bang, though lack of intuitiveness may make it seem so. To assert such a time, is essentially to deny that the universe has a beginning--a reasonable theory I suppose, but it is not the BB theory. And, the notion of time without beginning does have conceptual problems of its own.
The BB is ultimately just a simple hypothetical backward projection of the observation of the expansion of the universe. It must also incorporate the rest of physics, which appears to show time inextricably linked to mass and space. Physics is a mystery at certain energy levels and scales, so the BB theory is not well conceived all the way down to "a point".
When you say you disagree with the BB theory, is it the observation of an expanding universe you disagree with, or do you suppose there was something more complicated than simple expansion that occured in the past? Do you find an infinite universe easier to conceive of than a finite one?
To answer your question directly - I am a young earth creationist...I reject both the idea of an infinite universe, as well as the idea of a "BB."