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10 weeks at the earliest usually, by 12 weeks for sure. It's harder to hear early on if you've got some extra belly fat or a "deep uterus". They have a little machine that they scan over your pelvis and later when you're further along over your belly and they use a jellyish goo as lube and to help the sound carry. It's easy and painless- unless your dr or nurse is pushing hard trying to find it, then it can be uncomfortable. But really, it's one of the best parts of being pregnant :)
I have always heard my baby's heart beat at 6 weeks when they do the pelvic ultra sound.