Great question. I can relate. My first career out of high school was my dream job as well - the military.
How to stand out. The hiring team will want to know the answers to questions like;
What do you know about ABC?
Why do you want to work here?
What do you do for self improvement?
Where do you see yourself in 3 - 5 years?
Have genuine, authentic, and compelling answers. Saying, "ABC is my dream job" meets your needs but it wont necessarily meet there needs.
How to stand out? Have just as many genuine and thought provoking questions for them.
If you believe in ABC's culture, then you likely believe in very similar values and behaviours. You'll want to demonstrate you possess those same values, beliefs and behaviours from past experiences.
Consider coming to the interview with your own perspective on improving their existing product/service/experience or even something new.
DO NOT LOOK or SOUND DESPERATE! Think of it in terms of dating... you see someone from across the room and you think to yourself; they would be amazing to dance with, go to dinner, marry, and have 2.5 children. If you say that to them... you're going to look pretty desperate so play it cool. Be confident but not cocky. Be chivalries but not a door mat... etc... get my drift?
And hey, as good as this company is... there are always more great companies out there.
One thing is for sure, culture fit is key you your success as well as theirs. Good luck... you're half way there :)
You need to show them that you can solve their problems.
The #1 mistake made by most applicants is that they keep talking about themselves: "here are my skills, here's what I've done, etc..."
Instead of talking about yourself, talk about them:
"You need someone who can jump right in; someone who can start working without making mistakes. You also don't have a lot of time for training. I can get started right away."
This is going to require some research. Follow the founders / managers on Twitter. Read their blog posts. Scan their error logs (if they're public). Find out where you're *needed* and highlight that.
Generally it's best to do this during the application process. If you've already sent in a cover letter and resume, it doesn't hurt to send a follow-up email that says: "I've been doing some research, and I think I've found some places I could be helpful."
Think of 10 things that company could be doing. Write them a letter explaining what they are and why it might be material to the company.
Be sure you couch this at the top as "I have lots of ideas and I'm excited and I care" and not "I think I know how to run your company better than you do."