Is There A Way To Successfully Send A Text Without Knowing The Provider?

Well if you mean by provider is the cell phone company of your friend then you can't send a message to your friend until you know the provider. There can be many same numbers with different service providers so you need to know the exact provider.

I guess I don't know what a texting site is, free or otherwise.  You can send a text on your cell phone to anyone with a cell phone whose phone number you know.  I can't imagine why you'd need to know the provider if you are simply sending cell phone to cell phone.  I suspect that is not what you mean though, so my answer is probably no help whatsoever.   There certainly are not "many same numbers with different service providers" in the US.