“”How can the New Covenant cover them at that time when it had not happened yet?””
By believing the OT foreshadows and represents the coming Christ
Those who accepted the foreshadowing of Christ before Christ in the OT are covered by Christ and are “the people of God.” Scripture says no Salvation without Christ(Acts 4:11-12) thus,some people of the OT are covered
Acts 4:11-12 says....This is the stone which was rejected by you the builders, which is become the head of the corner. [12] Neither is there salvation in any other”. The typology from the OT is ....“The stone which the builders rejected has become the chief cornerstone. This was the LORD’s doing; it is marvelous in our eyes.” (Psalm 118:22-23)
Here is a good article from Association of Hebrew Catholics
The Church - Prepared for in the Old Covenant
http://hebrewcatholic.org/FaithandTheology/On-People-Israel/churchpreparedin.html
People from the OT were covered when they kept their covenant.