Is it possible to determine the gender of a person on the first visit to the site? How?

Question

Google Analytics

The task is to display certain content (or, say, change the appearance of the site) depending on the gender.
Is it possible to extract this information from cookies or in some other way from the browser?
The question did not arise out of nowhere. For example, the Yandex metric (counter), somehow, gets information about a person's age, region of residence. Perhaps based on public IP information ...
*ps ideas like "ask a question directly", or "log in through Ph.D. social network" do not work

Answer 1

Yandex metric (counter), somehow, gets information about a person's age, region of residence

They only assume it based on the analysis of search queries. It is unlikely that a woman will search Yandex for "dick enlargement reviews." A region is assumed by its IP.
There is no direct, 100% reliable and accessible way to implement it, and you obviously will not get access to the request logs.

Answer 2

Not "in some way", but according to the very specific technology of Yandex Crypto. Read about it, everything will become clear.