Getting the website to to the top 10 is not that easy. It requires a lot of onsite and offsite optimization works. You need to get more quality backlinks from authority websites.
it is a hard work but it is possible. you need to get back-links, write fresh and interesting contents every day, and etc.
i think to in top 10 of google search engine not difficult. The google Search Engine rank sites according to the number of access that site. Due to if your site have the number of access is large, it will in top 10 or 20 in short period of time. I think so.
It's almost impossible to get top ranking in a short time, unless your keyword is not a competitive one.
If you use a .com or .net or any top level domain,you can get in top 10 or 20 on Google but for your free domain i think you should build quality backlinks