People have been outright lying about suicides for a long time.
If it's counted as a suicide rather than an accident then maybe. I would then ask who is lying.
If it's faking deaths then that's the coroner system which you would have to question.
It's kind of undeniable that there's a rising mental illness crisis in the US and undoubtedly more suicides, but keep in mind that suicide, like all symptoms of mental illness, is hard to track accurately. Especially as the stigma towards mental illness is starting to cede.
When looking at data, an otherwise healthy 20 year old, and an 80-something with multiple chronic and/or terminal Dx's, would stand out.
The challenge in looking at population-level data is that the Dx may well not be available, though other indicia might suggest this (e.g., residence is an assisted-living or long-term care facility). In practice, studies are frequently limited to available data, and proxies are frequently used. These may not be appropriate for specific individuals, but at scale, the law of large numbers and general correlation are your friends.
In 1999, teen (15-19) suicide was at around 8/100k, and it's now around 11/100k. It's lower in absolute numbers than in the general population, but there's still a disturbing uptick.
https://www.charliehealth.com/research/the-us-teen-suicide-r...
But it would be extremely unknowable whether or not they had experienced suicidal ideations, and how long they had had them. Because the most you will get is a note in the medical chart, based on a verbal claim by an unreliable narrator.
The reasoning being that it's very difficult to hide bodies, and that statistics on suicide tend to point to some very deep-rooted pathology within a society.
Yes, it's possible to fudge those statistics somewhat (the distinction between "accidental" and "intentional" deaths being salient), but far less so than other indicia of psychological trauma, particularly at population levels (the focus of sociology).
But you can do that. Throughout much of the 20th century (in the United States, at least), the cops might be willing to just call it an accident (he was cleaning his gun) or an unsolved homicide. Ostensibly to spare the family shame or to allow the family to bury them in the cemetery of their choice.
Furthermore, there seem to be factors that cause upswings and downswings in the suicide rate. There were alot more people jumping out of skyscraper windows in 1929 and 1930 than there were in 1925 and 1926, for instance (though we might expect the opportunity to have been roughly the same). Now, that doesn't directly rebut your argument here. But it would mean you'd need to show that if there is an upswing today that it has lasted longer or otherwise been worse than similar ones in the past, or that it doesn't seem to have the same sorts of causes.
If possible, it might actually be better to pick some other measurable event/behavior than suicide. Psychotic breaks, schizo episodes, or voluntary commitment.
Suicide is an example. You can't "overdiagnose" suicide unless you outright lie that it happened. The rate for suicide was something like 10/100K in 2001 and is hovering at 14/100K now. This is a significant increase.
If more people are killing themselves, it's almost certain that there are far more people are also miserable or struggling than there used to be.
This seems like pretty direct reasoning, but I suppose it could be flawed.