Most young children are naturally empathic. But the majority of them lose the ability over the years as they grow up and become adults. From there it has been estimated that 10% of humans are empaths.
Both of my kids are now teenagers and their empath skills are growing very strong. But I personally think that a lot of that is because my wife and I support their abilities and are helping guide them through this. Conversely, our society and pretty much every religion does it's best to shut down empathy. We all know the typical stories of parents telling their kids that they really don't have an imaginary friend or that the bumps and whispers in the night are just the house creaking. That teaching moment training kids to disbelieve what they hear and sees sticks, and kids then begin to block their natural abilities. Whereas if you tell your kids you believe what they tell you and support them, their abilities will grow.
But to get back to your point, my daughter was the most obvious. I didn't know what an empath was back then, but I knew she had some unusual gifts and sensitivities. When she had her 1st birthday we had about 40 parents and kids over to celebrate. And she couldn't handle all of the attention and noise from everyone so after an outburst of tears we let her spent the rest of her party playing quietly in her room. We now realize that she couldn't handle the energy of everyone at her party. It was too much for her. And then while she was a little older but not yet able to talk, we used to hear her talking to no one in her room at night. We'd find her sitting up in bed staring at the ceiling having a very detailed conversation in baby talk with something unseen. And it got stranger from there. When she got old enough to talk, we would hear about her seeing ghosts all of the time.
I would say probably the thing you will notice the most with an empath kid is that they are very sensitive and introverted. They don't like to go out places and get fussy or anxious when out in public.