Spring or fall is the best time to seed. I am not sure what that means for your climate. However, you can seed any time. It just stresses or delays germination if it is too hot or too cold. Obviously you need to provide extra water if it is hot.
Hydroseeding will speed things up and establish a lawn faster than sod for a fraction of the cost. With hydroseeding a slurry of mulch, seed and fertilizer gets sprayed on your prepared seed bed and it forms a crust.