Can this drain pipe be moved back closer to the exterior wall
With the wider perspective and builder's drawing it is looking like your original assumptions are correct--the vent was intended to be in a wall parallel to the foundation. This is unfortunate, since moving it outward would require that the toilet stub also be moved. It needs to be centered 12&quot; from the finished wall behind it. The tub drain is also in the wrong spot if you're putting in a full 60&quot; tub.
So yes, if you wish to maximize room size, you'll need to open the floor. Unless there's some weird surprise under the slab, like an oversized footing, this shouldn't be a problem.
I'm not sure it's worth the effort, though. You probably want your wall in front of the upper horizontal run of pipe so you don't have to deal with working around that. This means you're ~4&quot; from the vent at the floor anyway. It looks like your basement is wide open otherwise, so that 4&quot; in a bathroom probably isn't consequential.