Yes, it is very possible. There are still a great many people in the world who “value” moral values. Good companies are always looking for people with a sense of ethics, integrity, honesty, and a commitment to work hard.
Step number one is get a good education. Step number 2 is find a field that offers opportunity for growth. Step 3 find a company that “fits” you. Find a company that values integrity and family (it’s not as rare as you think).
Also, have a career not a job. Sometimes you will have to make sacrifices (along with your family) in order to build your career so that years from now. When you are young, you need to look at building your resume for 3-4 years down the road not for immediate income.
Don’t fall into the trap that you have to do “something you love”. Almost no one gets to do that. Don’t sweat it, that’s why there are hobbies.
Above all, work hard and pray hard.
Oh, as for my job, I am a Regional Director of Sales for a very large company. It took me 9 years after college to get to this level. The higher I progress, the more fun the work is because it is much wider in scope and control. Unfortunately, it is a great deal of work and some travel, but the benefits definitely out weigh the costs.
Let me know if you have anymore questions.