There's no clear amount of time. It's not a rejection until it's a rejection. No response really just means that your resume hasn't been looked at.If you went through to the final interview for an internship position, it likely means that you did fairly well. When you apply to Google, make sure that the person who's reading your application knows that you previously applied and got through several interviews. It'll likely work to your advantage. This would be a good place to use a cover letter. If possible though, work directly with your prior recruiter.