That is incorrect. The old covenant was made between God and Abram, back in Genesis 15. God's specific references to Holy Days such as Passover and the Sabbath do not show up until the time of Moses, several hundred years later.
There are several covenants that have been established. When I use the term "old covenant", most understand it to mean the covenant established with Israel at Mount Sinai.
Heb 8:7 For if that first covenant had been faultless, then should no place have been sought for the second.
Heb 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Heb 8:9 Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Heb 8:11 And they shall not teach every man his neighbor, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
Heb 8:12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
Heb 8:13 In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.
The heart of the old covenant was the 10 commandments, given at mt. Sinai.:
Exo 34:28 And he was there with the LORD forty days and forty nights; he did neither eat bread, nor drink water. And he wrote upon the tables the words of the covenant, the ten commandments.
The holy days are first mentioned and instructed before the Israelites struck this covenant.