From personal knowledge it can happen pretty fast. My parents were married a week after they met. That was during WW II but they were happy together the rest of their lives.
A friend of my wife and I met the sister of another friend when there was a weekend long gaming get together at her house. The sister was visiting during college break. Our friend like us was a year or so out of college. They talked until they fell asleep on the couch leaning on each other. When he left Sunday evening she went with him. They got married a year and a half later and they've been together about 20 years now.
My wife and I decided after dating several months in college we'd get engaged after I graduated. We did and thats 25 years ago.