I was wondering if a Chevy 305 engine will fit in a 1973 Mustang?
You've got 1978 in the thread title, and 1973 in the thread body. Those are totally different cars other than most of the name and the manufacturer. It could probably be made to fit either one, but as
@jozsefsz said, the '73 would be a lot easier out of those two.
That said... why?
A Chevy 305 has zero advantages over pretty much any other engine in the history of engines. It provides all of the weight and fuel economy of a Chevy 350, all of the performance of an 80s-90s Chevy V6, and isn't even a good starting point for performance upgrades due to it's unique bore, weak crankshaft, and relatively small displacement and low redline.
Objectively, all of the other Chevy small-block V8s except the 4.3L smog-era V8 and the original 265 with no oil filter and block-front mount bosses are superior to the 305. Hell, objectively, so are all small-block Fords except the 255, and all small-block Chrysler V8s.
Even if the Chevy 305 is free or already on-hand; financially it's a bad decision as well, because you'll be looking at a lot of custom and one-off pieces that you'll either need to fabricate yourself (and if you're asking us instead of just doing it, I'm going to assume you don't have the tools and knowledge), or pay someone to make.
If you have a Mustang with no engine, and the Chevy 305 engine, the smart decision it to sell one or the other and find something compatible with the one you keep. This is a Mustang site, so suggesting to keep the Mustang would be a bit obvious, but to be honest, if I had a running 305 and could offload the Mustang more easily with the result being enough funds to buy something cool like a '67-80 GM pickup to drop it into (somewhere a 305 would actually be a pretty decent choice, as it's got enough displacement to be torque-y enough for the job, and will still sound great with a set of headers and dual exhaust, and most of it's limitations don't really hold it back), I'd totally keep the 305; otherwise, well, then the obvious choice for a Mustang site is obvious.