The phrase "having never" is correct and usable in written English. You can use it to indicate that something was true up to a certain point in time but doesn't hold true anymore. For example, "Having never won a competition before, it was a special moment when he finally took home first prize.".
He departed having never beaten Real Madrid.
He died in 1953, having never heard his masterpiece complete.
Only Death never changes, having never been away.
He was planning to visit France, having never done so.
SOMETIMES a team comes to the Super Bowl having never played one.
I once said that Caribbean cruises are meh, having never been on a Caribbean cruise.
Having never been to any of Mr. Robuchon's restaurants, I commanded a feast.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.