I assume this is before the first date?
I’ve had many shiduchim where the girl was asked first, or both of us were asked at the same time. I can’t think of even one case where the shadchan waited for me to say yes before asking the girl. I’m Israeli but I can’t say if it’s like this with everyone here.
I got the impression from a friend that with the Datyim Leumyim you ask the guy first and only once he gave his answer you ask the girl. Many meet on their own, but if they are set up by a friendshadchan it’s done this way.
Personally I see no reason to get offended by being turned down before the first date. Usually no one gives a picture, and the reason for being turned down could be related to the family (E.G. the father isn’t well liked in the community) or there was another suggestion which superficially looked more appealing
If you’re talking about after the date, the shadchan will usually call the guy first for his answer (so the girl isn’t turned down after giving a positive answer)