Why does Sourcetree not create a .git file in my repository?

[Trinity Lynne Harris]

I am new to Sourcetree and am using it as a student for a class. I have created a GitHub account and a Sourcetree account. After setting up all the settings after the initial download, I connected my GitHub account to the Sourcetree app. After that, I created a folder in my local directory (on my machine, I'm using a Mac) to hold all of my files. I cloned my GitHub account through the URL and connected it with the folder I had just created on my device. Upon getting the repository to show in the Sourcetree app, I checked that folder I created. Within it, Sourcetree (I assume) created a README.md file, but there was not .git file created (as shown in my teacher's instruction sheet). After creating a plain text document (and saving in the folder on my machine), staging the file and committing, I tried pushing the change to my GitHub account. I get an error message saying the push was completed with errors and to see the above message (which explains the push was denied). I'm not 100% sure how the Sourcetree app "communicates" with GitHub, but I am assuming it is through that .git file that is not being created in my local folder. I'm just wondering why this file isn't getting created (on my teacher's instructions for how to set up the account, it shows one getting created automatically, and he experiences no issues) and if this is the reason for the push not working.