When they were designed is unknown. Since they’re not considered superweapons like the Death Star, they didn’t get their own book detailing their design. There’s some evidence that they may have been in the pipeline as early as 11 years before the Battle of Yavin:
“The thorilide triangle,” Skelly said, astonished that she hadn’t
heard about it. He moved across the room to the other side, with his
wall of corporate shame. “The mining firms are corrupt. They’re tied
up—ownership, boards of directors—with the shipwrights that have sold
the Empire on one construction project after another. Oh, it’s all
being done in secret, but you can’t keep everything secret. A billion
Star Destroyers isn’t enough. They’re building Super Star Destroyers,
and Super Super Star Destroyers, and who knows what else!”
A New Dawn
Though this information comes from an unbalanced conspiracy theorist, his use of the term Super Star Destroyer seems a little too coincidental, and he was right about some other things.
They were almost certainly built and deployed, though, between A New Hope and The Empire Strikes Back, since they didn’t appear in A New Hope or Rogue One, but they did participate in the Battle of Hoth.
As for numbers, we do know that there were thirteen Executor-class dreadnoughts (a.k.a. Super Star Destroyers) in existence before the second Death Star was destroyed.
She starts with the Dreadnoughts—the Super Star Destroyers.
Thirteen were in service before the revivified Death Star was
destroyed above Endor. One of those is the Ravager, the SSD from which
Sloane rules the Empire (and which, strictly speaking, is now Gaelan’s
command). One of those is the Executor, Vader’s command ship. The
Executor was lost that day, plunging into the surface of the Death
Star. Taking hundreds of thousands of the best Imperials with it.
While we can’t rule out the possibility that the Rebellion destroyed some before the Battle of Endor, or that some might have been lost to other events or actors, it seems likely that they weren’t, and so thirteen is probably the number of Executor-class dreadnoughts that were built.