The time it takes for your website to appear on page 1 of Google depends on a number of factors. It depends on the search phrase people are using to find your website and the number of other websites that are also available for those search phrases. 


Nobody can truly say how long it will take for your website to appear at the top of search engine results pages (including people who actually work for Google), however there are a number of factors that can improve your chances. 


Building your website on WordPress is a good start as WordPress has some great Search Engine Optimization fundamentals built-in. 


Creating unique and interesting content on a regular basis for your website is also critical to increase your visibility among search engines. Launching your website and then forgetting about it is a surefire way to get lost among the noise.