Everyone wants there website to come up in position #1 on the first page of Google results. Is this a realistic expectation? Yes and no.
For the most part, depending on what the subject of your website is, you may have a tough time competing with already established websites to obtain that top ranking. Google and other search engines give preference to long established websites that are blessed with a healthy number of quality, inbound links. Also, a new website can take anywhere from a few months to a year to start showing results in the Google index. Google does this to make sure your website is a legitimate, viable resource rather than a fly by night website that is here today and gone tomorrow (their main intention being to leverage search engine results unethically).
That all sounds pretty grim for a company starting out with a brand new website. The good news is that there are some things you can do to promote and build up your website presence while waiting for Google to take notice.