Yes and it's a good thing imo because then they can use it to self-soothe. My first did this and she's now 3, no teeth or speech issues and October baby has been doing it for a couple of weeks. Now he can self-settle to sleep and re-settle himself throughout the night.
My little ones hands are never out of his mouth. Although I have noticed him try and get his thumb but he normally has it tucked between his index and middle finger. He sucks more on his index finger 🤣 I personally was a thumb sucker as a baby and through early childhood, had no issues with speech or teeth!
It is normal 🤗 don’t worry All baby’s suck their fingers 🤗 Mine is 4 months too all day long with hands in mouth 😅😅 I know is just a phase . I am trying to limit though this thing I bought some teething toys my baby loves them