The Duke and Duchess of Sussex stepped out Thursday evening in Los Angeles ... repping their Archewell Foundation at The Kinsey Collection art exhibition hosted at SoFi Stadium.

From a brief clip from the event, Meghan can be heard singing the organizers' praises -- saying she hopes their hard work will be recognized ... and that their success will be proof that they deserve all the praise they receive. Harry stands by as MM made her remarks.

TV personality Shaun Robinson posted pics of the couple at the event for the Kingsley Collection, which is currently touring L.A. with its African-American Art & History Collection.

She added the caption ... "Great discussion last night supported by @thearchewellorganization and Duke & Duchess of Sussex" -- while continuing to thank Harry and Meghan for coming out and supporting.

Their evening out comes just one day before Kate broke her silence on months of speculation over her health Friday ... announcing her cancer diagnosis, which was discovered after her abdominal surgery in January.

In her video statement, she explained doctors initially thought her condition was non-cancerous but discovered that cancer had been found in the aftermath -- and she's now in the early stages of preventative chemotherapy.

Just last month, Buckingham Palace confirmed King Charles was diagnosed with cancer ... so with all that heartbreaking health news, ya gotta wonder if Harry and Meghan may find themselves spending a lot more time in the UK in the foreseeable future.