The Jews were chosen by God because of his promises to their ancestors Abraham, Isaac and Jacob.
Their continuing existence is witness to God and his purpose:
10 “You are my witnesses,” says the LORD,
“With my servant whom I have chosen;
that you may know and believe me,
and understand that I am he.
Before me there was no God formed,
neither will there be after me.
11 I myself am the LORD.
Besides me, there is no saviour.
12 I have declared, I have saved, and I have shown,
and there was no strange god amongst you.
Therefore you are my witnesses”,
says the LORD, “and I am God.
Their selection was confirmed at Sinai and involved the nation’s obedience to God’s laws:
5 Now therefore, if you will indeed obey my voice, and keep my covenant, then you shall be my own possession from amongst all peoples; for all the earth is mine; 6 and you shall be to me a kingdom of priests, and a holy nation.’ These are the words which you shall speak to the children of Israel.”
As a kingdom of priests, their role as God's witnesses should have been to show to other nations the benefit of keeping God’s laws:
6 Keep therefore and do them; for this is your wisdom and your understanding in the sight of the peoples who shall hear all these statutes and say, “Surely this great nation is a wise and understanding people.” 7 For what great nation is there that has a god so near to them as the LORD our God is whenever we call on him? 8 What great nation is there that has statutes and ordinances so righteous as all this law which I set before you today?
Moses warned the people that they would be scattered if they disobeyed God:
64 The LORD will scatter you amongst all peoples, from one end of the earth to the other end of the earth. There you will serve other gods which you have not known, you nor your fathers, even wood and stone.
Their witness to God would be seen in their punishment and also in their continued existence despite being scattered among all nations:
10 Therefore don’t be afraid, O Jacob my servant, says the LORD.
Don’t be dismayed, Israel.
For, behold, I will save you from afar,
and save your offspring from the land of their captivity.
Jacob will return,
and will be quiet and at ease.
No one will make him afraid.
11 For I am with you, says the LORD, to save you;
for I will make a full end of all the nations where I have scattered you,
but I will not make a full end of you;
but I will correct you in measure,
and will in no way leave you unpunished.”
Their punishment and subsequent blessing is a continuing witness to God at work in the world:
23 I will sanctify my great name, which has been profaned amongst the nations, which you have profaned amongst them. Then the nations will know that I am the LORD,” says the Lord GOD, “when I am proven holy in you before their eyes.
36 Then the nations that are left around you will know that I, the LORD, have built the ruined places, and planted that which was desolate. I, the LORD, have spoken it, and I will do it.”