Oh dear, there is often such a failure of imagination about this on the part of “people who use words” (and I am one)! This is hard.
Deaf people don’t need “words” to form their thoughts. “Words” are their second language - their first language is “Sign”. Their use of it to form their thoughts, opinions, feelings, view of the world is almost incomprehensible to people who use “words”. Because, inevitably, the mass (majority) of people who use “words” automatically assume that “speech” is superior in every way and somehow essential to being human. Therefore, anyone who doesn’t automatically use “speech” must be inferior, or disabled.
This is why discussions like this always slide from wondering how Deaf people frame their thoughts without “words” to talking about how a pride of lions manages to communicate without “words”. It’s also why calling Deaf people “deaf and dumb” is so incredibly offensive, with its connotation of “dumb animal”. Deaf children have historically been treated as “pre-word” and almost like “dumb animals”, being made to sit on their hands to stop them using their first language (Sign) and to force them to learn an alien language (Words/Speech), which amounts to child abuse. Much of Deaf history is shocking and horrible, due to the arrogance and tyranny of “word-users”.
Deaf people have to learn “words”, of course, for convenience in a world that is entirely built around speech. Many Deaf people can and do learn to speak, although their speech is usually very recognisable as “deaf speech”. Many of them these days have cochlear implants, so that they can “hear” speech in some form for convenience, but this does not mean that they accept that speech is superior to sign (and the surgery has been a hotly disputed topic in the Deaf world for years). But their first language is Sign, and they regard themselves not as a disabled group, but as a linguistic minority, disadvantaged by having to live in a world where their natural language is hardly acknowledged. This is why there is a distinction between “deaf” (person who has lost some or all of their hearing) and “Deaf” (usually born deaf and uses sign).
This subject is, as you can see, somewhat of a hobby-horse of mine. Because of a profoundly deaf friend I embarked on learning BSL. Naively, and arrogantly, I thought that you learned the sign for a word, then substituted the one for the other. In fact, you have to learn a totally different method of communicating ideas and a totally different world view. It is both fascinating and incredibly difficult for anyone who hasn’t grown up in contact with the Deaf world, but very much worth it.
It is also very difficult to explain properly, and I suspect that I have failed here. I just hope any Deaf forum members and lurkers will forgive me!