There is the possibility of creating a responsive website without using a framework, however using them will make your life easier and consequently save time by having several things "ready". I do not recommend using it if you are a beginner, I believe it eliminates one phase of learning.
I have developed projects with several frameworks among them, BootStrap, Foundation, Semantic Ui and currently I do not use because the code is not always well organized, I do not use so many classes and the semantics used is horrible.
One cool tip is to read some of Mobile First, Media Queries, Relative Measures. Do not use gambiarras in the project, the organization in the initial stage will help you a lot during the process.