By the way, the name you have chosen always impresses me--byfaithalone--because it really is, by true faith.
This is the evidence that I have seen. The old covenant had every detail of the new covenant. This old covenant system was the "rehearsal", or the schoolmaster, the teacher, of the new covenant. There was a distinction that God directed Moses to perform in the preservation of the two distinctly separate laws.
The 10-commandment law was the character of God, by which sin was defined originally. After God wrote it with His own finger, Moses was instructed to place the tables of stone inside of the ark of the covenant in the Most Holy Place, which was the second room of the old tabernacle. The ark of the covenant represented God. By these tables of stone written by God's finger being placed inside of the ark, Moses was to illustrate God's very character and nature which emanate from within Him. It is what He is. In a Scripture study of the characteristics of God, and the characteristics of the law, one finds that they are both described by the same adjectives--holy, just, perfect, good, etc.
"And he wrote on the tables, according to the first writing, the ten commandments, which the LORD spake unto you in the mount out of the midst of the fire in the day of the assembly: and the LORD gave them unto me."
"And I turned myself and came down from the mount, and put the tables in the ark which I had made; and there they be, as the LORD commanded me." Deuteronomy 10:4, 5
Incidentally, they are still there, safely hidden from human eyes, but in God's appointed time, in the judgment, He will bring forth these tables of stone and present them before the world. Please read 2 Machabees 2.
There the prophet, Jeremiah relates the history of how he hid the ark and the tables of stone, and describes the time when they will be brought forth again and presented to the world. It's very interesting!
Now, as the solution for the sin problem, God designed His plan of salvation, which was given in precise detail to Moses.
"Who serve unto the example and shadow of heavenly things, as Moses was admonished of God when he was about to make the tabernacle: for, See, saith he, [that] thou make all things according to the pattern showed to thee in the mount." Hebrews 8:5
He wrote all of these particulars in a book and placed them on the side of the ark.
"And it came to pass, when Moses had made an end of writing the words of this law in a book, until they were finished,
"That Moses commanded the Levites, which bare the ark of the covenant of the LORD, saying,
"Take this book of the law, and put it in the side of the ark of the covenant of the LORD your God, that it may be there for a witness against thee." Deuteronomy 31:24-26.
This law typified the solution for sin, rather than being the actual character of God, as were the 10 commandments.
In fact, God clearly stated His feelings about their observances of the feasts and the sacrifices, showing that these feasts were not part of His character, although many in Israel assumed that they had salvation in all the killing and slaughter of beasts.
"Your new moons and your appointed feasts my soul hateth: they are a trouble unto me; I am weary to bear [them]." Isaiah 1:4.
Now, back to the new covenant--
"But this [shall be] the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
"And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more." Jeremiah 31:33, 34.
This wonderful promise is exactly what the new covenant is all about.
"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:
"And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
"For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
"In that he saith, A new [covenant], he hath made the first old." Hebrews 8:10-13.
Although the old covenant was nailed to the cross, the prophet, Isaiah shows that the plan of salvation will still be remembered in the new heaven and the new earth by worshiping God on the new moon and on His glorious 7th-day Sabbath.
"For as the new heavens and the new earth, which I will make, shall remain before me, saith the LORD, so shall your seed and your name remain.
"And it shall come to pass, [that] from one new moon to another, and from one sabbath to another, shall all flesh come to worship before me, saith the LORD." Isaiah 66:22, 23.