Well, I just did a quick google search, and it appears that the core of our own galaxy has a density of about 10 million stars per cubic parsec. Already, even at that relatively low density, we see signs of some very energetic phenomena occuring, although that may be the end result of 10 billion years of evolution at this high density. Perhaps if the creator really did create all the stars only 6000 years ago it would be possible for them all to exist within a 6000 light year radius sphere without having yet formed a super massive black hole.
However, many of these stars are pretty effing big and bright. Note that most of the galaxies are too distant to be seen with the unaided eye -- I would expect that if all those stars really were packed into a density of 100 billion stars per cubic light year the night sky would be fairly bright -- at least if the stars were evenly distributed, so that 100 billion stars were packed in the cubic lightyear that surrounds us!
My main concern, though, would be obvious gravitational interactions. We should see signs that the galaxies are attracting each other. And noting the intergalactic interactions with clusters of galaxies, which are pretty far apart, can be clearly observed, the lack of obvious graviational interactions between most of the galaxies that we see would seem to show that they are indeed very far apart.
Unless they were not massive suns as we understand them. I'm not sure how to answer your question. The color of the stars can be measured -- that gives some indication as to their surface temperature. Now, assuming black body radiation (which should be good to an order of magnitude) this would tell us the brightness per surface area of the star. If we assume that these stars are closer than 6000 light years, this would indeed put contraints on the size of the star.
A rough calculation: the brightness we see (assuming a point source) is proportional to the surface area and inversely proportional to the the square of the distance. Since the surface area is (roughly) proportional to the radius of the sphere, that means that a given star's radius is proportional to its distance (very rough estimate). So, take a sun-like star in the Andromeda Galaxy, about, 2 million light years away. If it were only 2000 light years away, that would reduce its actual radius by a factor 1000 -- if we previously assumed that this star is like the sun, with a radius of about 700,000 km, this would mean its actual radius is about 700 km.
And of course a "sun-like" star in a galaxy 1 billion light-years away would only be a few tens or hundreds of meters across.
And to prevent observable gravitational interactions, their masses would have to be very small, too.
It would be an interesting question as to what would be maintaining the surface temperatures that we see! Maybe they are really just very large LEDs?
Is this the sort of answer you were looking for, jar?