If you are lucky and start your project with a week before Google update and also have a great content then you may have a surprise but otherwise, it can take some time. The conclusion is that no one can tell you exactly how much time it will take.
Dont worry about PR for a new site,work on building your backlinks and new content and over time it should start getting a PR although its quality visitors that interest me more than PR.
Pr is outdated by Google for up to 6 months so it's really hard to say just focus on marketing your website and the PR will come. I would just use it as a guideline too and not gospel.
Google updates PR in irregular intervals, It might be tomorrow or even the next year, so don't bother about it
Find ways for your site to slowly gaining rankings and traffic, after then PR will follow once update happens.
No need to bother about the PR for a newly launched sites. You do what all you have to do to achieve good PR. When the time comes google ll look into your site and give you a PR. Until then keep working on your site's content and backlinking too.
continue working on your site and continue gathering quality link juice, and your PR will raise, remember long-term>short-term, work hard and you are sure rank! =D
Its difficult to mention any time frame.I have heard many people get a better PR for their new site just after the PR update.It mainly depends on how well your site is optimized for the Google and how unique your contents and quality of your backlinks.