Should I  start a relationship with a girl who I knew I couldn't stay with?
Why do you want to be with a girl you can't stay with?
I really like the way she looks
You don't have to date everyone who looks good to you. It's wrong to mislead people and toy with their feelings.
Women are known for saying yes to first dates anyways, I'm just manipulating their emotions.
That girl is going to see through your intentions and despise you for that. In fact you can not win over people by manipulating them. you should leave her alone and try to make real connection with people.