I'm a firmware engineer/manager in a large multinational tech company and have done hiring. Feel free to send stuff to me via PM if you like.
My opinions, which I used successfully to get hired where I'm at now but are possibly worth what you paid for them:
It helps a ton if you know someone or even someone who knows someone at the target company. Network, ask around, let people know you're interested in working at this place. If you find someone, just let them know you're applying for position X there, and did they have any general advice they're willing to give you. Listen to their answer.
Research the position - know what the company does, who their main customers are, what their main products are, what issues they face, and the hiring manager's name and job title.
Don't put anything in the resume or cover letter that doesn't relate reasonably to the position.
Cover letter should explain how your skills and experience apply to this job.
Customize both cover letter and resume for each position. Start with a generic one, cut-and-paste from older ones, but spammy "Here's my resume, do you want to hire me?" makes you feel good but is not effective and thus a waste of everyone's time.
No typos, grammatical mistakes, alignment issues, slang, anywhere. Have multiple people review what you're going to send.
Resume should be one page maximum unless you've got a work history over 10 years long and it's all relevant to the position.
