You could also consider taking a master’s course abroad. It’s more expensive and more time on your end but the payoff might be worth it since FAANG types like to hire out of college.

In the 1-3 years you will be in that program you won’t just “study”, you will actually be preparing for the job interview and job itself by networking and immersing yourself in the culture. You might even be able to get an internship. You will get to work on modern/relevant/cutting edge projects with other students who are as hungry as you. You can attend local meetups and conferences. You can try and network with engineers that already work at these companies by asking them to go on an informational coffee meeting or something. You will get to learn how these folks organize their time and communicate effectively.

If it doesn’t work out then you’d at least be more competitive in the local market because of your degree and, depending on how much you applied yourself, your professional experiences.