Really good question!! It is good that you are aware about recruiting and it is unfortunate that your desired company does not recruit from your university. Despite this little roadblock, there are still ways for you to network with and meet individuals from your dream company. I am not sure what year you are in college, but I recommend that you intern with your dream company if you still have time. Internships will provide you a way to directly work alongside with current employees and this can give you great insight into a possible future career. Also, companies often make full time offers to their interns which is good news for your (I was an intern that was offered a full time job with my past employer). This happens often enough where you should definitely do your best and be on your A game as you don't want to potentially squander a great opportunity like that.
Also, try and leverage who you know and your larger professional network. You'd be surprised regarding the number of people that you know who could provide you with a way "in". You may have a distant friend or a relative who knows someone who could set you up with a coffee meeting or something. It may seem like something small and inconsequential, but little meetings like that can often lead to establishing a professional relationship where they may be more willing and able to help you out. Everyone knows a surprisingly high amount of people, use who you know to your advantage!!
I hope this helps and I wish you the best of luck!!