This is possible to do. I've seen many people who are new to version control get started in GitHub online. I've also seen people whose workplace limits what they can install on their computer in strange ways. Here is how to make a new branch from an old commit online directly on GitHub's site right now.
- Go to the home page of the repository and click to see the list of all the commits on the repository. That button is surrounded by an orange square in the picture below.

- Click to browse the files of the commit you're interested in. This commit starts with a "3". That small button on the right is surrounded by an orange square in the picture below.

- Make a new branch from the commit. To do so, look at the place the branch's name usually appears. You can see this is the same commit - it starts with a "3" too. Click on the dropdown next to the commit number, type in the name of the new branch and click "Create" to create the new branch. Those fields are surrounded by orange squares in the picture below.
