There are lots of different routes into big engineering and space companies. Lots of people will do a degree at university in engineering or science and then get a first job in an aerospace company, sometimes on a graduate scheme which will help with further training (that’s what I did at Airbus). Other people will do an apprenticeship in engineering with a company, that way they get their training on the job instead of going to university, a great option if you prefer hands on work or really don’t like exams. Some apprenticeships even allow you to get your degree while you work, which is a combination of both options.
It is worth remembering that many people who work in engineering and space start off with jobs somewhere completely different and move into these companies later in their careers. Also, the big companies don’t just need engineers, they need people to work in their finance department, recruitment and media so there are loads of different kinds of jobs needing different skills in the space industry.