How does one ensure their knowledge of a field is complete when doing a literature review

This seems like an impossible task.

You're right, it is impossible. One can really never hope to gain a "complete" knowledge of a field, or even a subfield. You just have to do the best you can, in the time you have, to identify the most significant basic work related to your area of interest, and work that specifically addresses the questions you are studying.

Part of your advisor's job is to help with this; they should have a broader knowledge of the field, and be able to help direct your literature search and point out any glaring gaps. But despite your combined best efforts, there will almost certainly end up being significant work that you overlook, or whose relevance you don't recognize. That is just part of doing research. Someday you'll learn about it and wish you had known it earlier, but all you can do is move on from there.

It is impossible to capture everything in any field of academic literature, but the good news is that you don't need to. To proceed, you need to have a clear view of your purpose for conducting a literature review (other than, "I have to, as a grad student"):

1. For your own learning about the relevant knowledge in your field
2. To help you narrow down to a concrete dissertation topic
3. To publish a summary that is helpful for other researchers

On one hand, these are three distinct goals that require somewhat different strategies. On the other hand, since they are all related, it is possible to combine these three goals and achieve them all with one general strategy.

I recommend that you target your dissertation topic, and to do it in such a way that you gain relevant knowledge in your field and can publish a summary of your review that is useful to other researchers. You could proceed in this general way:

• Begin with a good idea of what topics interest you (you must like your dissertation topic!) and also interest your doctoral supervisor (your supervisor must also like your dissertation topic!). (If you don't have a supervisor, then make it a priority to get one right away, or else you can easily add a few years to the length of your doctoral program.)
• Conduct literature searches on one definite topic of interest. You must target a concrete topic. It is when you try to find "everything" that it gets overwhelming and impossible. Your goal in searching is to find the seminal research (that is, the research that is most highly cited) and the most interesting unanswered questions. They must be interesting to you for the sake of your intellectual engagement, and they must be unanswered so that you have the opportunity to make a real contribution. (That said, your supervisor should help you later on to add one more requirement: feasibility. It must be practical for you to answer the question within the timeline and resources of a doctoral dissertation--your supervisor can help you assess that.)
• When you have a concrete topic from these literature searches, do related searches for literature that is related to your topic and might have some bearing on it (treatments of the same topic in other disciplines, potentially relevant methodological approaches applied to different topics, etc.)

Hopefully, with a general outline like that, you should be able to advance. Again, the result would be a concrete dissertation topic, you will have learnt relevant knowledge along the way, and your publication of your findings should be helpful to other researchers.

Also, note that my outline was sufficiently general that it should be applicable to almost any academic discipline.