When creating a new repository on github, you want to be sure to NOT initialize it with a README. Otherwise, when you push your existing repo, you will get errors which will require you to do a force push that can create problems later on.
So just make sure to keep the README checkbox unchecked.
Then initialize your project in case it isn’t.
git init
Add all the files in the folder
git add .
Commit them
git commit -m "initial commit"
Connect the project to remote repo on github
git remote add origin https://github.com/user/repo.git
And finally push all the changes and files
git push origin master