Writing a letter of recommendation for a promising but very new student
As suggested by @academic in a comment, I think this is a case where you should decline to write the recommendation (and do so as quickly as possible so that they can find someone else) and suggest they ask someone with whom they've had more interaction.
I think it may end up normal for students during the pandemic to rely on recommendations from instructors they have had less interaction with due to the obstacles of online learning, but here you're talking about someone for whom you can't even refer to their performance on a single assignment.
If you wrote a letter that was honest, really the best you can do is to write what you've said here: this student meets expectations for an attentive student in the limited interactions before the first course assignment is due. I can't imagine that letter filling any positive role besides checking a box towards &quot;x/N letters submitted&quot;. If acceptance for the internship is competitive then the letters written for this student will be compared to letters written for other students, and a non-robust letter like yours will probably compare unfavorably.
Additionally, as a PhD student you might also suggest to the person asking you for a recommendation that they get letters from professors rather than graduate students. It's possible that the distinction isn't as important for this internship, but generally references from professors are preferred. When I was a graduate TA I would occasionally co-write a letter with a professor in charge of the course I was teaching: the letter would come from the professor, but I'd add my own paragraph that the professor would incorporate into their letter. I don't suggest you use that for this situation (and it doesn't make sense if you are the instructor of record rather than a TA), but something to keep in mind for future requests.