Yeah...you don't have much real world experience, do you?
If you like someone I strongly suggest you be friends with them first for like a year
If you want to torture yourself and risk infinite friendzoning, sure.
Don't start by asking to lunch or coffee.
Unless you feel like having a nice afternoon with someone you're attracted to, sure.
Most girls are either taken or not looking.
Completely wrong, but sure.
create a scenario in which you are forced to interact.
Yes, because overthinking things make everything better, so sure.
Girls:
You have it easy gtfo.
Not true, but our society has developed the idea that requires men to initiate interaction and dating shit, while women are supposed to wait because if they took the role of "asking out" it could be seen as too forward or even creepy. But with women becoming more and more independent, these social stigmas are likely to change.
You obviously have yet to be introduced to the concept of "Risk and Reward".