Cookies sent on first request to a website after deleteting all cache/cookies - how is it possible?

I am trying to create an HTTPWebRequest using c#, as part of the request, I store and manage all cookies request. For some strange reason, I have one cookie that is missing and this causes some problems. This cookie appears starting from the first request to the website (Not the first response). Can anyone please tell me how is it possible? The web browser is clean so where is this cookie coming from?

I have noticed the same behavior from different websites, here's one for example: http://ift.tt/2cUCT74 , on this site, the G2JSESSIONID cookie appears on the first request to the server

Does anyone know where this cookie is coming from?

Thanks