There are sentences in English like "What's up?" "What's going on?" "how have you been?" to begin a conversation with or to greet people (friends or relatives)
So what are the common ice-breaker sentences in Chinese?
Here are a few ice-breaker sentences:
最近怎么样？（Literally "recently how"? = How've you been recently?）
最近好吗？（Literally recently good?）
最近忙什么？(Literally recently busy what? = What have you been busy for?)
The weather is a good topic for people living in a city.
When you see someone you know but they seem busy:
你怎么样？ - How are you?
(for a person you just met) - 你是哪里人？ - What province are you from?
If you here mean "ice-breaker" is " Something that can break the ice while talking in a senario or environment that makes people very stupid or embarrassed. You can say:
1) 没和我开玩笑吧？(Are you kidding？！)：Used when you feel ver surprised at something or something very awful that you don't expect to happen.
2) Invite someone to have a dinner with you (Even if you are not good with someone but you wanna have a talk with him, that's what Chinese people are glad to do).
However, if you wanna know something to be used when you wanna start a topic with a man not familiar to you, here are some tips:
1) 可以借个火吗？(If you see the man is smoking, you can say this to have a talk with him for the following things). 2) 你好，饭吃了吗？(You don't need to invite him/her to have a dinner but just a greeting sentence for your following talk).