It’s a skill and like any other skill it becomes less anxiety inducing the better you get at it. You could start with complete strangers at (say) a coffee shop, so that if you get embarrassed well it doesn’t matter, you’ll never see them again (this is how I improved). Also, learning how to be rejected and bail out is part of the skill. I still get into awkward situations sometimes, but it’s happened enough that I can cut the conversation off and the embarrassment doesn’t bother me all that much