I'd thank her, kiss her back and see where it goes from there. I might be able to save the cost of dinner and movie tickets.
MEN answer please: If on a first date, the woman walked up to you, right as the date started, and kissed you (to possibly remove that awkward what if feeling), what would you do?
Throw up a red flag. In my experience women who are too forward leads to problems early on. If this happened to me it wouldn't be a good first impression.
It really depends on the situation. I don't think anyone can just say a very certain answer. Depends on the person (which the person you choose should completely depend on who you are, cause this is a fail if you go on date with someone that their world would be clearly far away from you) then depends on the place,circumstances & the most important the manner & behavior behind the movement & the kiss.
(However i never been & i'm not into dating & dating with different people) .. But in a normal condition, that kiss would be fine, even more than fine, i like when a girl can be confidential enough to make things forward, i hate awkwardness, i totally hate it so her kiss is welcomed, she showing that she's comfortable & i'd be too, & i'd be happy about her comfort, i'd kiss back gently & will take her hand & will continue to the date & will save one kiss on her hand for later on, at least a simple kiss is better than walking a thousand times & not saying nor doing anything. I'd die rather than having silent awkward, discomfort , stressful (in fear of what if i do something that things mess up) date.
I'd skip the hors d'oeuvres and head straight for the main meal.
That depends ... Is the woman who walked up to me, the one I'm going on a date with? 'Cause if not, that would be awkward. Lol
Seriously, though. I'd be offended that, before the first date, she thought she knew me well enough to do that. Even if we had talked for years online, that's too much of an assumption. I'd cancel the date and have to think a long time before I continued any relationship with her.