I have had the experience of getting the 30% ruling a while after I started working - so retroactive requests are not a problem (though they might be if you cross the boundary of a tax year; not sure about that point).
However,  a Master's degree and being under 30 merely reduce the salary minimum to apply the 30% ruling. As explained, for example, here, the criteria are (emphasis mine):
- You must be an employee of a company in the Netherlands.
- You have specific professional expertise that is scarce or not available in the Netherlands. Highly skilled migrants are deemed to have such expertise when their income meets the salary requirements.
- You and your employer agree in writing that the 30% ruling applies to your situation.
- You have been recruited or transferred from abroad (and you have lived more than 150 km from the Dutch border for more than 24 months prior to working in the Netherlands.)
and as @Gala points out, the salary limit is lower for people with a Master's who are under 30.
So it looks like what you need is some kind of agreement or confirmation from your employer that you qualify. I don't think you can apply for the 30% ruling on your own without employer involvement.