Looks cool, but is there any reason sentences on the website don't begin with capital letters? It is a youth thing?
No. Do not do this.
Because capital letters are mostly omitted when the writer is in a hurry and doesn't care very much for details, which is insulting to the reader in a context where care and attention is expected.
And if you hadn't thought of those reasons - the fact that everyone else does should be a clue. Chesterton's Fence and all that. Show some humility!
Gretchen McCulloch has a book called Because Internet which talks about how the internet has changed English. People joined the internet in different waves. Each group of had the challenge of re-inventing writing conventions for the writing that falls outside of the relatively formal academic/business writing taught in highschool.
For the people were using a cellphone with autocorrect was a significant part of their internet usage, uncapitalization became a way to indicate casual tone. Since autocorrect would capitalize for you, it was clear that the lower case letters weren't the result of you being lazy. Instead you were going back to deliberately undo the capitalization of the word.
So yes, it is probably a youth thing and it's done to indicate a casual tone.
Stylistic choices and a casual tone are one thing, but nearly everyone who reads English is thrown off by this particular choice. Style should almost never take precedence over forcing your readers to put effort into actually reading.