He has gone to America.
This sentence denotes that “He” went to America and is still there. Probably he has moved and started living there.
When you use “been” in the sentence, “He has been to America,” it denotes that he went to America and, after some
time, came back. He is not in America anymore.
So, "has gone" never be used with "since".
Have you gone to the cinema recently?
Yes. I have gone to the cinema three times since January. (Note that "I have been to" works as well.)
My grandmother has gone to Finland a couple of times since my grandfather died.
My boss has gone to a meeting every day since the beginning of March.
What you will notice is that along with "gone to" and "since", each one of those sentences contains a timescale statement ("three times", "a couple of times", "every day").
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.