We had hundreds, if not thousands of those tiny black Weevils (long nosed grain weevils) in our basement. We don't keep any food in the basement. We were told by experts and exterminators, they were just coming inside to get out of the cold. However, had a nagging feeling that there must be a food source somewhere, but could find no food source for those little black bugs.
My family dealt with those bugs (and pesticides) for four months, then finally, I found their food source (after searching for months). We bought a Bean-bag toss, and the bean bags were stored in the basement (and filled with indian hard corn). I got rid of them and finally, no more bugs. Who would have guessed it was the bean bags? I cut a bean bag open and found hundreds. Just remember, if you are super infested, they must have a food source.