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The website rank in the search engines can be increased by writing quality content, promoting the website, writing blogs and regularly updating it. Promotion through social medias like Facebook, twitter, LinkedIn, Instagram and many others. On page SEO and Off page SEO togeher will improve the website rankings in the search results.
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Continuously monitor your site using Tools like SEOSItecheckup, Google Analytics, Google WEbmaster Console to check if there are any errors.
Try to Submit High QUality Content on High quality sites.
Do guest POsting on Sites With High Domain Authority.
Build quality backlinks using your primary keywords as anchor text
Do a proper site audit using tools like WEbCEO, SEMRUSH and get all the issues resolved.
Although doing above doesn't guarantee that you will rank on the first page but you will certainly increase your chances of ranking some where on the first page of Google.