It will take a lot of work. Many people "dream" to work for prestigious organizations but find out that they can find some cutting edge work in other places. Don't limit yourself to just a few organizations at first. If they don't hire you, that just means you get to spend a few years honing your skills in similar work before re-applying. Good luck.
I want to first congratulate you on pursuing your dreams
If you want to land your dream job and it is in the cyber-security world you first need to figure out what is the dream job you are looking for. Another thing is that you at least want to get your foot in the door. You might start doing tier-1 analyst work for a year, but depending on your development then you will move up roles.
Additionally, go on linkedin and search for people who work at both organization in a role you're interested in. Send a short and polite message stating you're a student and would like request some of their time to learn more about working at their organization and their career journeys. Not everyone may reply but if some may. Use it as an opportunity to learn more and politely ask if they can recommend you for an internship if they have the capacity.