Please try logging out of your Upwork Desktop App, close the app, open it, and log back-in. This should refresh the app, and your contract should be listed already.
If it doesn't happen automatically, let us know so that our team can assist you further.
While your contract was accepted on March 19th, it will become active on Match 29th. This is the date when it will become available in your Desktop App. Kindly, communicate with your Client about this, and attend to clarify any possible ambiguities.