In her book The Emergence of the English, Cambridge professor Susan Oosthuizen argues that our entire understanding of the Anglo-Saxons is based on outdated and disproven assumptions, that recent developments in history, archaeology, genetics, and linguistics indicate that we may have it all wrong, and that the Anglo-Saxons as we understand them may never have existed, and their invasion of Britain never happened. She gave a video lecture on it in 2020 which can be viewed here: https://vimeo.com/425282049. What are your thoughts on this? Are there any other academics who have supported or refuted her arguments?
This turned into more of a "state of the field" report so it may not be the most satisfying answer to your question, but hopefully some of this is interesting to you!
The trouble here is that using an ethnic, racial, and/or cultural identity to explain historical causation is always going to be problematic. A lot of scholars of late antiquity and the early medieval period in England are doing a lot of the same work as scholars of the Viking Age. That is, trying to deconstruct the misconceptions developed by Victorian antiquarians who were in the business of romanticizing their Germanic forbears.
One of the struggles that scholars of late antiquity and the early middle ages in Northern Europe and Britain face are racialized tropes and stereotypes developed between the 16th and 19th Century, particularly by Victorians, who wanted to draw a connection from a deep, heroic Germanic past to their contemporary burgeoning global empire, and doing so to justify their global hegemony because it's somehow due to their superior Nordic spirit. The Victorians heavily racialized this mythologized version of English and Northern European history, and unfortunately, that concept of an actual race called "Anglo-Saxons" basically stuck in the popular imagination throughout the Anglosphere. Even well-meaning and recent scholarship falls into this racialized version of history, as you see in this article, which applies anachronistic understandings of race and racism to the so-called Anglo-Saxon period.
At any rate, a lot of what Oosthuizen says is not particularly new in this field. However, as you can imagine, the field is pretty small, and, perhaps more significantly, very arcane and in some cases, very elitist and exclusionary) So, because of this, it's not often that ideas from the field hit mainstream awareness, and when they do, they are almost always mired in controversy of some sort or another. However, not all is hopeless, as very forward thinking scholars have been making great headway in the field for a while. There are still some very deeply held beliefs about "Anglo-Saxons" that just aren't going to go away any time soon.
The popular belief about Anglo-Saxons among students in my experience, is that, if they know anything at all about the period, is a very simple version of the story. Romans pulled out of their holdings throughout England, the defenseless Romano-Britons, out of fear of being conquered by the "less civilized" northerners, invited the Angles, Saxons, and Jutes to serve as auxiliaries, but then two enterprising brothers, Hengist and Horsa figured they'd just conquer the helpless Britons themselves. So, if that's the version of the story that you were left with after graduating, hearing something like what Oosthuizen is saying probably sounds wildly unorthodox, perhaps even iconoclastic. However, as the links above show, people have been thinking in this same vein since at least the 70s. There's been a lot of work in reevaluating how exactly the culture and language of England became seemingly more Germanic over time. The consensus has generally moved away from a largescale military invasion that unilaterally supplanted local cultures, and has moved more towards the idea of elite replacement, but even that is problematic. Increasingly, there is more evidence for cultural hybridization. As the example Oosthuizen gives of the Sutton Hoo ship burial, we can see that pretty clearly, where you see British methods of enameling (coating an object in glass) and objects that bear remarkable similarity to Vendel-era Swedish material culture, which doesn't necessarily mean there's a direct connection between Sweden and England at the time, but that there were people in these areas that were in a cultural orbit throughout the North Sea that may have centered around Denmark. Whether that culture came to influence culture in England was due to a large invasion of Angles, Saxons, and Jutes, or due to cultural osmosis through multicultural trade throughout the North Sea, or some combination of all of that, is still up for debate.
Anyway, to really get at the heart of your question: Did Anglo-Saxons exist? That depends on what we mean by that term. Do we mean a culturally homogenous race that held itself distinct from the local Britons? Probably not. Do we mean a culture and ethnic amalgamation from around the North Sea world that, after prolonged contact with Romano-Britons in some form or another, caused cultural shifts in England? That's more likely. There's no doubt that Old English was in use and that people indeed called themselves Angles and Saxons (which is preserved in placenames around England: Sussex, Essex, Wessex and...England). Literary evidence also shows us that, whether or not they were ethnically Angles, Saxons, or Jutes, people who wrote down Old English poetry were certainly writing down poetry that is very much Germanic in its meter, its rhetorical devices and so forth. The biggest thing to understand is that Anglo-Saxon culture may not have been imported and forced upon the local populace, but it was more of a process of hybridization. You don't need to be of a certain ethnicity in order to speak a specific language, or even to adopt the habitus associated with a particular culture. The question though is how exactly it happened, and that's something that is going to puzzle us for a long time.
Note: I've linked to several book reviews, rather than the monographs themselves to give you a quick overview of some of the things I'm citing. Happy to provide more direct citations if desired!
In addition, you might be interested in Why did the term “Anglo-Saxon” stick around into contemporary times when there’s been 1000 years of that culture being mixed with the native Celts and absorbing the Danelaw settlers and other Scandinavian influences while also being dominated by the Norman conquerers and everything else? contains a synthesis on the term written by u/sagathain as well as links to previous answers by u/kelpie-cat and u/Steelcan909