It is a little tricky in the work place.
If you see someone in passing or break room & want to say hello, you don't necessarily have to have eye contact, although it would be nice.
If you think the person would sincerely appreciate a "hello how are you doing" or "how are ya today" then go out of your comfort zone, give it a whirl. You never know, you may give them a reason to smile.
If their response isn't so positive, move on, try not to take it personal. There are other people in your work place. Take some deep breathes & with another person take the opportunity to try & be friendly again.
If one or the other doesn't start a convo then there won't be one. Again step out of your comfort zone, "how's your day going", something simple. There doesn't have to be eye contact for that either.
Keep trying, you sound like a nice person.

Good luck.