Even if you feel they don't understand your language, tell them soothing, supportive things like: "It's OK," "I'm here," "I know this is hard."
I learned this from my father who was a sort of baby whisperer and that's what my friends call me now.
I got this by watching him and also being the recipient of this treatment, I remember crying because I was just anxious or bored and always wishing it would be my dad who came. Babies adored him, and kids flocked to him because he always had a relaxed demeanor with kids and communicated that he was interested in them and took them seriously.
As an aside, my father was a physician and people always asked why he never became a pediatrician because kids loved him and he loved them. He would always answer along the lines of, it's because he loved them that he couldn't do it, to be a pediatrician means you have to hurt the kids and that's very hard when you empathize with them so much.
Your heart may be full of empathic stress for the little one, but don't show it in your body language or facial expression, they know.
ETA: This is really just advice for a baby in existential distress, not biological of any kind, including being sick or injured. Though soothing is often helpful even in these cases as well, it shouldn't always be the only way you address their issues.
At the beginning of the year I was living at Mom, no money, no job, smoking a pack of cig a day, lost in mind, lost in soul.
Today I have my driving licence, my car, already 8000 kms in it, a job which I am about to leave for a better one with such a paygrade raise, the difference itself almost covers my monthly rent. BECAUSE I MOVED OUT AGAIN, I live with this wonderful man I wish you would know. You would love him. I know.
I am happy Dad. I truly am! This was a hard year but a wonderful one, filled with love, memories ( I remember again!!! I can remember Dad!!! My mind loosen up and let me remember!!!)
I AM SMOKE FREE SINCE APRIL! IT'S HALF YEAR!
And last Sunday I was able to provide help to our friend who broke her arm. I was able to pick her up and take to the hospital - she is fine-. I was able to drive such lenght, I left my home around 9-10 pm and arrived back home 2 am. I had to wait at the entrance of the ER for hours as they let only 1 plus in.
I just..... I made it Dad. I made it.
I wish you would made it too.