Moses was God's appointed leader and the Lord's messenger. He represented Israel before God, and brought God's word of instruction to the people. In the Lord Jesus Christ we have the only mediator between God and man.
1 Timothy 2:5 "For there is one God, and one mediator between God and men, the man Christ Jesus."
It appears that on the first going up the mountain that Moses went on his own initiative. His expectation was met with the Lord calling to him from the mountain (Exodus 19:3 ) giving him a message to deliver. Leadership that goes to the Lord expectantly in prayer, will be given the Lord's mind, will, and purpose for the people.
Exodus 19:3 "Thus you shall say to the house of Jacob, and tell the children of Israel:"
Behind the two names God looks upon His people in two ways - He sees us as weak, struggling Jacob - but also as the Israel of God complete in Christ.
Colossians 2:10 "And you are complete in Him, who is the head of all principality and power."
That the Lord Had Dealt with Them in Redemption and Grace
Exodus 19:4 "You have seen what I did to the Egyptians ..."
All our spiritual blessings are based on what the Lord has done for us. He paid the ransom with the blood of Christ. For we were bought at a price (1 Corinthians 6:20 ). He was slain and redeemed us to God by His blood (Revelation 5:9 ). He has released from the bondage of sin into the freedom of grace. (1 Peter 1:18-19 ). Therefore we are blessed.
Ephesians 1:3 "... with every spiritual blessing in the heavenly places in Christ."
Exodus 19:4 "... and how I bore you on eagles' wings and brought you to Myself."
The individual child of God can look back and see how he has been carried by the power of God, from the moment of his conversion, along the way of life to the point at which he now stands.
And brought you to Myself. We have been brought near by the blood of Christ. (Ephesians 2:13 ).
They were called upon to obey His voice and keep His covenant (Exodus 19:5 ). Sadly, they failed to keep the covenant. It was made in (Exodus 24 ) and the people promised obedience (Exodus 24:7 ). Christ has mediated a better covenant, which is established on better promises (Hebrews 8:6 ). The new covenant is contrasted with the first covenant, (Exodus 19:5 and Hebrews 8:6-13 ). Christ's blood is the basis of the new covenant. Believers have the laws of the new covenant written in their mind and heart (Hebrews 8:10 ).
First Privilege: A a special treasure to Me (Exodus 19:5)
There was a sense in which Israel was special. They were entrusted with the oracles of God (Romans 3:2 ), the Scriptures, the promises of God. They had the covenants, they had the law, and service for God. From them came Christ Jesus in His human nature (Romans 9:4-5 ).
Titus 2:14 "Who gave Himself for us, that He might redeem us from every lawless deed and purify for Himself His own special people, zealous for good works."
We are His own special people for special service - to be enthusiastically occupied with His good works. Serving the Lord of all the earth - for all the earth (Exodus 19:5 ). When the Lord specially blesses or makes one specially blessed, it is to bless all others through the blessed.
Second Privilege: A kingdom of priests (Exodus 19:6)
They failed to act as priests for God to the nations, to be channels of blessing and intercession. The privilege was taken from them (Matthew 21:43 ) and given to the church (1 Peter 2:9 ) who have become a royal priesthood. The Lord Jesus Christ is today a priest upon His throne. He has fulfilled the prophecy
Zechariah 6:13 "... So He shall be a priest on His throne ..."
In Revelation 1:6 the kings and priests are those whom Jesus Christ loves and loosed from their sins by His blood (Revelation 5:10 ). Are we reigning in life? (Romans 5:17 ). Are we properly exercising our priesthood? (Hebrews 13:15 ).
Exodus 19:6 "... These are the words which you shall speak to the children of Israel."

What is the intended meaning in the people being called "house of Jacob," and "children of Israel"?
Granted that you need to seek the Lord for a word for yourself, do you need to let that word overflow to others?
God focuses through His messenger on what He has done (Exodus 19:4 ). Do you attribute your obedience and spiritual blessings, all your privileges, to what the Lord has done for you?
Why does the Lord bring you to obedience by writing the laws of the new covenant in your mind and heart (Hebrews 8:10 )?