There were people from other nations also present at Mt Sinai
Ex 12:38 tells us, Yes, there were others. The end of this post explains how they ALL AGREE/placing themselves under the Sinai covenant.
BTW:
No one was under this covenant before they reach Sinai & no one is under it after Jesus tears the Temple veil in 1/2. Matt 27:51.
Read Ex 19:8 & my note below.
Point:
Rom 3:
20 Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.
(MY NOTE: The law teaches/exposes sin & by doing so, condemns the sinner to death)
21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
(MY NOTE: People become righteous before God thru Faith placed in Jesus, faithful, obedient sin redemptive WORK & resurrection. Not thru their own good works or law keeping)
22 Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
(MY NOTE: We access His imputed righteousness thru faith placed in Him/His faithful/obedient/righteous redemptive work. Found in His sinless death, burial & resurrection. Jesus Christ is the Lord our righteousness (Jer 33:16, 1 Cor 1:30, 2 Cor 5:1, Rom 1:17).
Mosaic law is just, BUT, it can't justify anyone. The law is holy, BUT, can't make anyone holy. The law is righteous, BUT, can't make anyone righteous.
The problem isn't the Law, it's our adamic sin nature.
Main Point:
So, if the law can't make us holy, righteous or justified, condemns a sinner, without mercy unto death.
Why, are so many people tenaciously driven. To place today's NT believers (who aren't under Mosaic law Rom 6:14, Acts 15:24) under Mosaic laws yoke of condemnation?
Rom 8:
1 There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit.
2 For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death. Best wishes, JJ
Reread Ex 19:8
Ex 19:
3 God, spoke to Moses saying, Thus shalt thou "say to the house of Jacob" "and tell the children of Israel";
(NOTE: God tells Moses, say to: the house of Jacob/children of Israel! Gentiles had/have NO PART in this law covenant)
6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
(MY NOTE: God chose Israel to be a Nation of Priests, to teach ALL the world His ways).
7 And Moses came and called for the elders of the people, and laid before their faces all these words which the Lord commanded him.
(MY NOTE: Law of Moses was given to: The house of Jacob/children of Israel (reread vs 3)
8 And all the people answered together, and said, All that the Lord hath spoken we will do. And Moses returned the words of the people unto the Lord.
(MY NOTE: "ALL" the people answered & said, "ALL" that the Lord hath spoken WE WILL DO! They could have said no & left, yet, THEY ALL AGREED to the words the Lord had spoken. So, anyone that wasn't part of the House of Jacob when they left Egypt, was now, by choice, part of this Sinai covenant.)