"The sentence 'snow is white' is true if and only if snow is white."
This sentence (and the others like it) defines a property of true statements. It does however not prove that there are true statements. Lets make a list of all true statements using the sentence you just quoted (and others like it) as a criterion. Let's say every sentence that the quote applies to is true (*). So we get: snow is white, snow is black ... and everything else. This makes no sense. Let's do the opposite and only accept sentences are true for which the quote doesn't work. We find that there isn't a single true statement.
That's basically just a complicated way of saying statements like these are completely useless outside of their specific context. It's perhaps useful to differentiate from other theories of linguistics that would say "the sentence 'I am hungry' is true if someone makes me a sandwhich whenever I say it" or something else) but that's that.
In any case, assuming that there are true statements, how'd you actually know which ones are? Since if you can't find a rock solid criterion even if there is "a truth" still noone would actually know. They'd believe in something which is coincidentally true.
(*) But is the quote itself really true?
The sentence 'The sentence 'snow is white' is true if and only if snow is white' is true if and only if the sentence 'snow is white' is true if and only if snow is white.
Hmm ....
The sentence 'The sentence 'The sentence 'snow is white' is true if and only if snow is white' is true if and only if the sentence 'snow is white' is true if and only if snow is white' is true if and only if the sentence 'The sentence 'The sentence 'snow is white' is true if and only if snow is white' is true if and only if the sentence 'snow is white' is true if and only if snow is white.
The sentence ...
... HELP IM STUCK!
