1. Start a blank Note (iPhone), Google Doc, or whatever. Call it whatever you plan to title your paper — for now. Put ideas here as they come to you.
2. Put the readings/lectures aside, think for a few minutes, and say your honest answer to the prompt. Write it in the blank document.
3. The blank document should sync across your devices. That means you can add to it whenever. You also can delete, re-word, and move text around.
4. When you are ready to write your paper, you can sit down at a computer and work from the document. You might even write the paper on the phone, but that makes citing sources more tedious.
Addition of October 25, 2023: Now that you have gotten started on your paper, please see this post on how to structure it.