In Northern Europe (Iceland, Norway, Finland, etc.) it is more the custom for women to do the pursuing/asking. But in the U.S. I can’t tell you how many men I’ve apparently offended or “emasculated” by asking them out. Americans are pretty steeped in gender roles and it makes for some pretty toxic gender-specific behavior.
My best relationships have ALWAYS come out of budding friendships, where we actually get to know each other a bit, grow some rapport and feel safe with each other before any dating happens. Most women I know would never consider a random man hitting on her, even if hot. It’s just not safe; stranger-danger is real. Once bitten by a dog, you will always fear any dog you don’t know. Stats show most women have experienced harassment and/or trauma with men at some point in their lives. Until men start checking other men behaving badly and turning the stats around, we can’t and won’t know who to trust.
Speaking for myself and many women I know, if I am out alone doing my own thing in public (like reading, taking a train, shopping, jogging, etc.), and I don’t know you, have enough respect to JUST LEAVE ME ALONE. My existence in public is not an invitation to connect.