In ranking for particular keyword searches, your website may or may not reach the first page. The competition surrounding a particular keyword phrase will determine how long it will take to rank. It will also determine how much work it will take to achieve that rank. SEO is a process. It's also a multi-level process that includes on-page optimization, backlinks, social media, PR, content marketing and more.
The best guess for ranking would be anywhere from 30 days to 6 months. Daily work on your strategy will help your move closer to your goal.