Can you write a thesis without a literature review?
Short answer: No, it is not possible to write a thesis without a literature review. The literature review is an important part of your thesis and helps you situate your research within the existing body of knowledge on your topic. Your supervisor will also probably tell you to add one if your thesis does not include a literature review!
When you sit down to write a literature review, the first thing you need to be clear about is that you are entering a particular conversation. To contribute to this conversation, you need to know what has already been said—in other words, you need to conduct a literature review.
This means that, at the beginning of your literature review, you need to have a clear idea of what your work aims to do and which gap in the existing research you want to address with your work. Only then can you start looking for material and begin reading purposefully (and conducting empirical research).

Literature reviews come in different forms
An important distinction in Step 2 is whether you do this systematically or unsystematically (“narratively”). If you want to conduct a proper literature review that can stand on its own, then a complete systematic review is the type of review you should choose. If you only need the literature review as a basis for an empirical study, a narrative overview is generally acceptable and more than sufficient.
Conclusion
Science is a dialogue, a debate. If you can deliver a theatrical monologue, that is fine, but it is not science or research. You cannot do science by only talking (researching) and not listening (reading papers).
But if you feel that you have to take this route, a very exploratory research question is the best choice.
Furthermore, I myself am certainly not a strong reader. I think it is about finding individual strategies that work for you. It definitely gets easier as you climb the career ladder. But even at the beginning, you can find collaborators who are good readers.
