How to ranked the new website on 1st page of search engine without backlinks?

It would be very dependant on the niche and how competitive it is, its more than possible to maintain good positions in long tail low competition keywords.

Compare their website with yours

• all on page Optimisation aspects
• Whether they are using any form of Schema or microdata.
  
• Are they taking advantage of Google Authorship
  
• How active are they on social signals
  
• Do they have any 301'd domains pointing to the site which do have backlinks but have not yet shown up

There is a considerable amount of things you can do to help a site with out backlinks to give you the best possible chance. You also might wish to take a deep look at your own backlink profile and make sure its not holding you back, its possible some of your backlinks could be having a negative effect.

With out knowing your site and your competitors i couldnt really offer any constructive advise.

 

Forget it. This is not possible.
You can use Adwords.... lol

 

Its not possible, but may be that website content is unique and meta title and meta description is good and unique properly on-page optimization also get in google 1st page.

 

Backlinks only can improve the keyword ranking.. New website need more backlinks.

 

Is it happen?

 

Yes with help of lengthy content , On Page optimization, schema markup tag (with the help of schema creator tools) you can achieve well rank in search engine.

 

Quality content is more important than numbers of backlink. Google always first refer those site which have updated and Fresh Content which was not found before.and onpage factor play important role in ranking new website.