How to be inviting to a man at church

A church member introduced this introverted guy in church to me, but he's really reserved. I only see him on Sundays, and I am interested but don't want to do the pursuing. I want to learn how I can invite and encourage him.

He has shown signs of interest in his own way, and this is also based on what my family and church friends have confirmed. If we have the chance to speak again, should I say that Im hungry and see if he asks me out for lunch, or should I do the asking to see if he's interested to grab quick lunch before our church event (usually after lunch)?

I think he's looking for signs to see if I'm interested, but we haven't had much interactions beyond surface level chats and id like to get to know him better to see if we can click. Thanks in advance for the advice!!