I'm wondering if there are any languages that are basically just streams of basic sound blocks, like letters or syllables, and they don't have words.
This raises the question, "what is a word?" Perhaps surprisingly, linguists don't have a solid answer to that question. The most common definition cross-linguistically is "a unit that's useful to describe how this particular language works".
However, all languages have morphemes (groups of sounds that have meaning), and in a language with no real distinction between groups of morphemes (like in Chinese) these would probably be considered words in and of themselves.
TL;DR: the concept of a "word" doesn't have a hard and fast definition, so it'll be defined in whatever way is most useful for any given language. If nothing else, a word can be defined to be a morpheme, which is a unit that exists in every language without exception. (Without morphemes, you don't have a language.)