I am an ECE graduate and have now worked for 17+ years in core domain across multiple companies - big and small.
I was lucky to get a first job in a core company (C-DOT) through campus placement. A lot of topics studied during graduation were not relevant for the job except for a few (like Digital Design, Circuits and systems, Communication and Networking technologies, Programming concepts etc). There is a need to continuously learn through your job/career as technologies keep changing demanding new skills . This continuous learning of new technologies and new skills is what keeps me motivated and makes the career journey exciting.
In the initial days of your career, there will be a lot of struggle. Things will be different from college. Lots of learning and re-learning of concepts will be needed. You will need to pick all tasks that come your way. You might like some tasks while a lot of others may not look interesting. The key is to establish your credibility in the team and build a foundation by doing above and beyond your tasks and learn as much as possible in the process.
After a couple of initial years, I decided to switch company for more challenges and learning and was lucky to find a job at Intel. Following basic principles of learning, delivering tasks to timelines and networking with other team members and experts, I could explore multiple projects ranging from networking chips to microprocessors designs and skills varying from silicon/system debug, FPGA emulation to RTL design and verification.
Later I also worked with a couple of semiconductor startups and continue to work with a mid size company today - all primarily motivated by opportunities for learning new technologies and challenges as well as working with some exceptionally talented people.
In short the quest for learning and hard work in early years will make a job in a core company turn into a fruitful career over the years and the overall journey will be very exciting and satisfying.
And not to forget, ECE engineers get paid well as entry level engineers and based on the effort you put and learnings and how you take on responsibilities through the the journey forward, money will follow and so will several other benefits.
Hope this helps.
PS: Here is a snippet to my career journey if you are interested which is part of a Verification career presentation that I gave early this year.
For a detailed blog post on same read following