Allow me, as a man, to offer some male perspective on that. Let's consider several possible reasons why a man does not respond as hoped when a reasonably-attractive woman is kind and friendly to him, with the intent to show "subtle interest":
The man, having heard many stories about men being shamed, ostracized, and even arrested for misinterpreting the signals, cautiously assumes that she is
just being polite and does not respond with interest.
The man, completely focused on the tasks at hand, simply does not pick up the signals.
The man, being interested in someone else, chooses to ignore the signals.
The man, being rather socially inexperienced, is not aware that the signals are actually signals.
The man actually is not interested in the woman, for any number of reasons.
Any of these, or others, could be in play. Don't assume too much. If you consider him worth the effort to break the ice, then
break it. Don't tap at it. If things don't work, at least you will have grown in experience.