Are all actually equal?
”We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”
The first thing to point out here that your title is misinterpreting what is said. All are not equal, but rather all have the same inalienable rights. The equality being discussed here refers to the bolded part in the above quote, it is not to be interpreted as people being exactly the same in every possible sense.
Furthermore, while you might consider it a nitpick, the document does not assert this equality to be a self-evident truth. The document merely relays that the authors consider this to be a self-evident truth:
We hold these truths to be self-evident
In a similar sense, if I write on a piece of paper that I believe in Bigfoot, that is not a document attesting to the existence of Bigfoot. The document would be attesting to my belief in the existence of Bigfoot.
What is the evidence for these claims?
I'm going to sidestep the above nitpick and for the sake of this answer assume that the document is both asserting the authors' belief and that the authors are implying that their belief is objectively correct.
I'm sidestepping the proof that "men are created" for obvious reasons.
I'm also sidestepping that this document is not a proof of empirical facts and is in fact closer to a manifesto of what is desired (politically, morally). The document claims self-evidence, which implies that these observations can be independently reproduced. TO that effect, we can infer that the authors are asserting some kind of factual consistency to these claims, even if the method is not rigorously defined.
With regards to the existence of inalienable rights, this is really a circular definition in that the rights themselves are inherently defined as applying unilaterally to all "men" (using the historical phrasing here, which nowadays is interpreted as "people", which is what I'll be using from this point forward).
This is, in essence, saying the same thing as stating that the fruits of an apple tree are called apples. Yeah, that's why we call it an apple tree in the first place. Similarly, it is "obvious" that all people are endowed with these inalienable rights, as a "right" (as opposed to a "privilege") is inherently defined as applying to all people.
In a way, the declaration is tautological in that it is stating that which is already asserted in the semantical definition of an "inalienable right" in the first place.
However, that observation is made with my 2024 eyes. At the time that this declaration was written, it was not obvious that rights should be unilaterally extended to all people (if you need an example, the same people ratified the three fifths compromise 11 years after the Declaration of Independence). The reason it's being pointed out explicitly is to distinguish it from what we nowadays call privileges, i.e. rights that can be changed or revoked by an overarching authority.
While this document does not offer explicit proof, it is being used much to the same effect that a peer-reviewed paper would be used: to stop further exploration of this subject, instead offering a final conclusion that people are universally endowed with certain inalienable rights, and that this conclusion should not be infringed upon, going forward.
As with all politically motivated discourse, whether you consider this correct or not is a matter of personal/political opinion.