You surely don't need God(s) for the creation of the world. You may need one for the creation of the Universe because physics doesn't offer something definitive and "quantum fluctuation of the void" is just a sophisticated concept to say "God did that" or "Randomness did that" what is in practice the same thing
But I like this kind of questions because they show that even a totally fantastic world has finally many hidden constraints that it must respect if it wants to stay logically consistent.
Unfortunately for civilisations our sample consists sofar of 1 sample what is not statistically significant.
Assuming that the evolution of life on earth is representative of most (not all !) life generating processes in the Universe then we can say :
- once liquid water existed, apparition of primitive life came really fast
- the life spent by far the largest part of its evolution in a primitive (archaea-eucaryote) form
So that gives approximately the following calendar in billions of years (I took some outrageous simpifying hypothesis in points where no unique answer is known) :
- birth of the Sun and the planetary system at 0
- creation of liquid oceans and plate tectonics at 0.5
- first archaea and photosynthesis at 1
- first multicellular at 2.5
- first land plants and bilateria at 4
- first intelligent species ancestors at 4.444
- first intelligent species at 4.4498
- first civilisation at 4.449994
- middle age (where your world is now) at 4.449999
So what you see is the hallucinating exponentialo-exponential acceleration towards the end. The Nature (or magics) needed 4 billions of years to go from nothing to worms, 200 millions to go from mouses to semi intelligent apes and 200 thousands to go from humanoids to civilisation.
So considering this to be a kind of standard, your oldest civilisation can't be older than a few thousands years and the planet not much older or younger than 4-5 billions of years (what implies a small sun).
An interesting case would be a total wipe out (e.g 100%) of all higher level species, civilisations included. In this case the nature would "spare" the first 4 billions years of evolution and would produce new intelligent species and civilisations in "only" 500 millions years or less.
If some small group of the inteligent species survived the total wipe out then their civilisation would be 500 millions years old. However in this case it is higly improbable that their civilisation would stay "stuck" in the middle ages.