Looking for general information on my watch

[DonO61]

Hello, Don from Montreal here, I recently purchased this watch from the grandson of the man it was presented to in 1968,
From my limited research I think it is a Cellini 8443
Now from what I have found Rolex introduced the Cellini model in 1968, but the serial number on the inside of my watch dates it to the mid 50's, so I'm confused, this is the one and only Rolex I own and I'd love the learn all I can about it