Everything not gravitationally bound is moving away from everything else. Every single point in space is growing larger. That means that things farther away from you are moving away from you faster then things closer to you. That’s true no matter where in the universe you are.
There’s not really an “away” from the big bang. That’s something science communicators fail to explain - the big bang happened everywhere. Space may have been infinite in size (we don’t know) and it still happened everywhere.
I’d recommend looking up the YouTube channel for FermiLab. They’ve got some excellent videos on the subject.