I have been trying to open your eyes to another possibility, so don't be ungrateful. The universe is infinite and eternal because nothing does not exist. The BB would only make sense if there was space already existing.
So you can believe the BB came from nothing, or you can consider a preexisting infinite universe (multiverse), up to you.
When you use the words 'came from', you are implying the existence of time. But time is part of the universe of spacetime. That is true whether or not time is finite into the past.
An analogy is to look at a globe and think of latitude as analogous to time and longitude as analogous to space. At any 'time' (i.e, any latitude), 'space' is finite (the latitude line is finite in length). 'Time' has a 'start' at the South pole and an 'end' at the North pole. Space starts as a 'singularity' at the South pole, expands until we get to the equator, then contracts again, ending in another 'singularity' at the North pole. The South pole represents the Big bang and the North pole represents a 'Big Crunch'.
Now, this is an analogy that is two dimensions down from what we see around us. In the analogy, 'space' is one dimensional (in fact, circular). In reality, it is (at least) three dimensional. But the basics of the analogy hold: the 'singularity' of the Big Bang is simply when time started. There is no 'before the Big Bang' in this model any more than there is a 'south of the South pole'. Space expands as time proceeds, and expands 'into the future'. As far as we know, the universe will continue to expand and not contract again (so the analogy is wrong in this particular--easy modifications can be made to make it more realistic--say a trumpet shape).