This question gets to the heart of current debates across the broader field of History. I caveat that I write this all from my perspective as someone who studies modern political rhetoric, most recently in post-communist Central Europe.
Historians receive all sorts of training about how to address sources, regardless of whether they're supposedly propaganda or not.* Traditional analytical questions often form the base of any historian's initial examination of a document. Who wrote it? When did they write it? Who was their audience?... and similar. These questions are crucial for establishing some basic facts about the document, and also for establishing what you may not know. For example, let's say you see a political poster in the archives but don't know if it was for the 1992 or 1994 election. Your interpretation may well be different depending on that reality, but it also could be relatively similar. In other words, even from the starting point, we run into problems with basic facts about the document.
However, basic facts don't necessarily tell a story. We have to ask questions like "Why did this person write this?" and "What are they not saying, or saying only subtly?" These are difficult questions to answer, even for a well-read historian who knows the subject matter very well to begin with. Finding a purely objective answer is nearly impossible; some historians will argue that it is truly impossible, and that the search for objectivity is worthless.
Others disagree, and say that objectivity can be a relative pursuit; they argue that we can and should accept the answer that is the most accurate compared to all potential answers [1]. This is understandably a matter of great contention.
Ultimately, regardless of your position on objectivity in history, you do need to do some digging, and you'll need your analytical questions to get there.
*In my field of political rhetoric, arguably everything is propaganda. It's almost easier to deal with your question of "truth," because a historian like myself presumes that most sources have some pretty clear agenda. As such, you can't rely on any one source for a baseline narrative, and to draw out any sort of "truth," you need to combine sources, even if you're just caveating and contextualizing the rambling diatribe of a retired politician.
[1] Bevir, Mark. "Objectivity in History." History and Theory 33, no. 3 (1994): 328-44. doi:10.2307/2505477. https://www.jstor.org/stable/2505477
Historians are trained to think about subjects in various ways and to question how information from the past still exists. We have excessive amounts of details on every US President, but millions of enslaved Africans and African Americans lived in the same country as these presidents with hardly any traces of their presence. As a discipline, we know this disparity comes from centuries of racism establishing a hierarchy to document/preserve certain lives while ignoring others. Stephanie Smallwood's article "The Politics of the Archive and History's Accountability to the Enslaved" focuses on how this process occurred and how historians can challenge entrenched power. Smallwood calls it reading against the grain. Our field can learn a lot from specific absences in the historical records when we know power structures in society determined who was missing from the record. For example, when reading against the grain, a historian might look at advertisements from enslavers offering rewards for the return of their property. But another way to consider this source is as part of a larger collection of advertisements. All the runaway advertisements from the southern US might show frequent routes taken by black Americans to escape slavery, which begs the question of how so many enslaved people know about successful routes. Runaway advertisements were originally a form of power against enslaved people, but historians can turn that power around to ask about how enslaved people created a communication network beyond individual plantations. Its the same sources, but historians can emphasize different voices.
Stephanie Camp's book Closer to Freedom discusses enslaved women's everyday resistance. Not every rebellion was bloody. Camp looks at how some women might take their time to fetch water from a pump. Its not a violent uprising and its not an obvious act of resistance, but historians can look for those spaces where black women could carve out brief moments for themselves. Silent resilience can leave traces, so historians take careful looks sources to find clues about erased people.
For a long time, pro-slavery forces wrote the history books (see Karen Cox's book Dixie's Daughters or this video here: https://www.vox.com/videos/2017/10/25/16545362/southern-socialites-civil-war-history). But historians study the history of history too, and we can challenge problematic historiographies. Kevin Levin's new book Searching for Black Confederates looks at how myths and histories formed to perpetuate narratives. We question our own field and criticize how history can maintain oppressive power structures.
More and more, historians are rejecting notions of objectivity to find these moments of resilience and survival in the lives on non-whites, women, LGBTQ people, and other oppressed groups. Our jobs are not to be objective keepers of historical facts, but to interpret the past to give greater meaning to the present. In our current moment where intersectional politics are so prominent and so many voices are escaping oppression to be heard louder and louder, historians need to look where those voices came from before now. Why did we not hear them before? Why are there silences in the past? Answering these questions can inform us how victors rewrote history to create a story, but asking questions to bring out new perspectives means that historians can resist the continuation of oppression.
I'm an archaeologist, not a historian; archaeology has sometimes been referred to as "the handmaiden of history". We generally don't really care for that label, but it's relevant here. There are other sources of historical information besides the texts produced by people directly writing about contemporary events. Where those sources give different information than the "propaganda", they enable us to make new interpretations as to what might have actually happened. As a hypothetical example, if the historic documents say that a group of people were peacefully relocated, and we go to that area and find hundreds of mass graves, with the bodies having items typical of the people who were supposed to have moved, with most of them having their skulls bashed in, then we have reason to believe that the historic accounts don't accurately describe what happened. Sometimes we refer to this as "hidden history".
Another approach (and perhaps an actual historian can comment on this further) is something like the Annales school of history, where secondary documents are collated and examined rather than looking directly at what people say was happening. So for instance, instead of reading an official announcement saying "we had a prosperous harvest", the Annales historian would go look at grain harvest records, market documents, and letters between local government officials to see if they talked about food shortages or surpluses. This gets hard in situations where these documents might also have been falsified, but it still lets you take an alternate angle that "cuts through the supposed propaganda".
Following are some examples of archaeological studies looking at "hidden history"; relevant to your question, you'll note that the people discussed in these studies are not "the victors" of their particular time and place.
Hansen, Joyce, Joyce McGowan Hansen, Siri Hustvedt, and Gary McGowan. Breaking ground, breaking silence: The story of New York's African burial ground. Macmillan, 1998.
Joshel, Sandra R., and Lauren Hackworth Petersen. The Material Life of Roman Slaves. Cambridge University Press, 2014.
Lightfoot, Kent G., Antoinette Martinez, and Ann M. Schiff. "Daily practice and material culture in pluralistic social settings: an archaeological study of culture change and persistence from Fort Ross, California." American Antiquity 63, no. 2 (1998): 199-222.
McGuire, Randall H., and Paul Reckner. "Building a Working-Class Archaeology: The Colorado Coal Field War Project." Industrial Archaeology Review 25, no. 2 (2003): 83-95.
Wegars, Priscilla. Hidden Heritage: Historical Archaeology of the Overseas Chinese. Routledge, 2016.
Here's one more thought I just had that is probably good to share: the idea that "victors write the history books" in its literal sense is a vast oversimplification that I would encourage any students of history to question. We have numerous examples where understanding of historic events was shaped by the "losers" rather than the "winners".
Some examples:
Most notoriously would be the Confederate "Lost Cause" and its strong influence on American remembrance of the Civil War, its causes, and its effects. The Dunning School is an example of this making its way into dominant discourse among academic historians, and would only be challenged in the mid-20th century (I would recommend David Blight's Race and Reunion for more information on how the memory of the Civil War changed in the 50 or so years after its conclusion).
History of the Eastern Front in World War 2, especially in the United States, was for most of the 20th century heavily distorted by the self-justifying writings of German Wehrmacht officers, as u/Georgy_K_Zhukov notes in this answer.
The Jacobite rebellions are remembered through a heavy filter of Scottish Romanticism (mostly courtesy of Sir Walter Scott), rather than a British/Hanoverian point of view.
In English-language histories, it is a challenge to get any Vietnamese perspective on the Vietnam War (or should it be Vietnam's American War?), let alone perspectives from North Vietnam and the FLN. And North Vietnam was the clear winner!
These are just some choice examples that might resonate with an American audience. In general I would highly question the premise that "history is written by the winners" - it tends to obscure more than it illuminates. History seems to be as much written by eloquent and influential losers as by winners.