Red shift has been demonstrated to be caused by objects moving away. The greater the red shift, the faster the object is moving.
And no, the background radition can not be explained by a number of 'radition objects' That is because the background radation is consistant, not coming from any one source. Radation from specific objects would vary in intensity. (i.e... just like stars to). The 'background' radiation is amazingly even. This would be consistant with a big bang.
The observation that caused people to conclude that the 'big bang' happened is that the objects in the universe are flying away from each other. As we took our observations, and extraploated back , the objects got closer and closer togather. BTW, The concept that is started as a single point came from a priest.. .. funny thing, huh?