How long will it take a new website to rank in Google ?
And by rank, you mean....? Just being seen and rank on top 10 page results, or within page 1 results, or being on the top 1? You gotta define your goals first, then break them into smaller tasks.
Without divulging your niche, we cannot really say our opinion even with a slightest hint. Among other things to consider are:
1. how well you optimize your site? if you go for very easy keyword, even if it is a crappy-looking, unoptimize website, you can def rank. otherwise, don't bother.
2. what is your method on backlink acquisition?
3. (related to #2) what is your budget for this? or do you have any budget at all? cause if you have budget, it makes things a lot more easier for you, while no budget, you have to do all the work, thus it will be slow process.
4. how do you plan your SEOing? SEO doesn't just mean purely backlinks. It is a game strategy and without out, a simple move can make a detrimental, irrevocable effect to your website.
5. what's your competition standing? check for your competition's status -- the backlinks, their authority, trustworthiness, metrics. and with the right knowledge, you can really know if it is a good keyword to go after or not.
6. how patient you are? those who are too aggressive with a NEW website may end up in sandbox if they don't do it properly. been there, done that, never do it again.
7. what time you can spare to maintain the website? personally I go around 100+ articles for each site. yes it is time-consuming, neck-breaking, brain-wrecking task, but it is what it is. a lot of affiliate websites are being done and sold every single day, so why does only a few appear on page 1? and it's not just about content, there are other stuff to consider in maintaining your website. not gonna mention it all though.
As you can see on my all other posts and replies, I always claims to generate income within 1-2 months from the time I build the site. My sites were never really rank for top 1 of my target keyword. For me, it's not really about "just ranking", it's about "conversion" and how many people will pull out money on their cards to buy from you or your websites. After all, isn't that what everybody wants, right?
PS. sorry for the typo/gram errors you can find, I am on phone atm and I'm sleepy as well.