Is it possible to Travel to Italy before September 1st? I'm from India

I don't have a passport right now. If I start my tatkaal passport process right now and then apply for Schengen Visa, is it possible for me to make it on time and travel before Sept 1? It's 18th of July the date I'm writing this. The reason for this time constraint is I have an exam to give on that date in Italy, the stay wouldn't be any more than 2-3 days max.