Actually, I have no idea about this.
Is good relationship a must before marrying?
Absolutely. Just like in real life you wouldn't meet someone for the first time and then ask them if they would marry you 5 minutes later. Well, maybe in a arranged marriage society that would be okay, but it's not the norm. "Hi, Swamachi, I jumped off of the tree of manhood, will you marry me? There's the Shaman over there."
Getting the Propose social is a progression in the game of increasing degrees of romantic socials you'll have available. As soon as you see a new one, get on it and keep workin' it. And don't just make booty calls the primary go to plan, if you know what I mean. Relationships thrive on other kinds of socials as well — like talking about things they're obviously interested in.