the time gap between SA and FT positions in post-MSc recruitment in London

I'm just a little confused and I'd really appreciate clarification. With regards to post-MSc recruitment in London, from what I've seen on LinkedIn, most MSc grads land a summer analyst position first and then a full time position later on. I'm not well acquainted with how recruitment goes, so can someone explain that gap in time? for example, I noticed specifically that people get full-time jobs in CS in April, in Citi they get FT in February, and so on

I'm asking this because after a MSc degrees I, as an international student, would not be permitted to stay if I don't have a ft job. So, I'd really appreciate someone clarifying that. Thank you all and happy New year!