Simple answer, "No".
The Game Bird Starter has all the proteins and vitamins that they need to get a great healthy start in life...unless you're an animal dietitian, chances are anything that could be made would be lacking a key component that is integral to the nutritional needs of your quail.
There are some folks that have done tons of research and purchase the ingredients, mix, and crush to quail sized bits...so it is possible...but they will tell you 1) They have done the research and know what to add ( I believe them) but 2) it is way more expensive that way than buying the "off the shelf" stuff.
A lot of organic breeders make their own, but it is not a cost saving action.
Good luck with whatever you decide.