The phrase "to strike up" means to begin or initiate something, often by starting a conversation or making an effort towards achieving a goal. Full definition
So at some point I just struck up conversation with him and he was very friendly. (brooklynrail.org)
I'm not usually the outgoing person who strikes up conversations, but maybe being a little more stylish will give me the confidence I need! (meijerstyle.com)
Use your imagination and invent your own original ways of striking up the acquaintance. (adult69personals.com)