According to the Weyland industries timeline
1) Hypersleep chambers were patented in 2030
2) FTL was discovered in 2032
3) First FTL ship was built in 2034
So it's possible that the Covenant was launched around 2035-2040 and had FTL/Hypersleep capabilities.
I guess it's also possible that it was launched earlier and was meant to be a slow moving sub-FTL multi-generation ship, but got sucked into a wormhole or some other space anomaly mcguffin.