I have heard this from many SEO experts that a website with less bounce rate will rank well on Google. But what if the website does not use any analytics tools to calculate bounce rate, how will then Google know the bounce rate of the website and rank it higher
Google does not use SERP bounce rate ("pogo sticking") as a ranking factor.
Google only knows the bounce rate for visitors coming from Google Search. They do not reach into anyone's Google Analytics accounts to get that info - besides, many websites do not have Google Analytics installed anyway.
Even though they know this bounce rate, they do not currently use this info except as a bulk data point to tune the ranking algorithm itself.
According to Google's John Mueller:
We try not to use signals like that when it comes to search. So that’s something where there are lots of reasons why users might go back and forth, or look at different things in the search results, or stay just briefly on a page and move back again. I think that’s really hard to refine and say "well, we could turn this into a ranking factor."
So I would not worry about things like that. When we look at our algorithms overall, when we review which algorithm changes that we want to launch, we do look into how users react to these changes. But that’s something we look at across millions of different queries, and millions of different pages, and kind of see in general is this algorithm going the right way or is this algorithm going in the right way.
But for individual pages I don’t think that’s something worth focusing on at all.
So while it's possible that pogo sticking could be a ranking factor for other search engines, it is not a ranking factor for Google.
As you are likely to be aware, a Bounce is where someone visits a single page on a website and then leaves. Often, this is perfectly normal. For example:
Example One: A browser visits a One-Page website. By design, all of the information is on one page where the visitor does not have any options to click through to any other page;
Example Two: Let's say a browser performs a search, looking for a Restaurants' Contact Details. The Search Results bring up URL
www.example.com/contact-us. The visitor clicks through to the page and then fills in the forms and leaves. There is no need for the visitor to click through to other pages as they have found the page they are looking for. Some would argue that a low Bounce Rate, is this instance, would not be a great thing.
As such, it would not make any sense for search engines to include a website's Bounce Rate into their Ranking Algorithms.
On the other hand, there is something known as 'Pogo Sticking'. This is where a visitor performs a search query and then clicks through to a website. They then immediately click back to the Search Engine Results Page (SERPs) and start to click through to other website pages within the same SERPs.
Unlike Bounce Rates, 'Pogo Sticking' could be a good indicator to search engines that the existing entry into the SERPs does not adequately meet the needs of the searcher or their search query. As such, a search engine may allow 'Pogo Sticking' to affect how a web page appears within the SERPs.
Google does not rely on Google Analytics installed on websites. They have their own means of calculating the behaviors and activities of websites that appear in their search engine.
Helpful Resource: https://support.google.com/analytics/answer/1009409?hl=en