The heart actually starts forming and beating very early, around 5 weeks after conception, but it's just a tiny flicker then. We first saw that flicker at about 6 weeks on an ultrasound. I didn't actually hear my babies' heartbeats until around 9–10 weeks at a scan, and my midwife didn't try with a doppler until about 12 weeks because it's hard to find before then.
There are at‑home doppler devices you can buy, but they can be tricky to use in the first trimester and often cause more worry than reassurance. I only started picking up a heartbeat at home around 10‑12 weeks, and even then it took some patience. If you do use one, ask your care provider to show you how, but otherwise the best way to hear that little thud is at your prenatal appointments.