God gave his word to provide faith to man. Faith comes by hearing the word of God. This does not mean audibly hearing only, it means to listen sincerely with the heart and believe God's word.
Rom 10:17 So then faith cometh by hearing, and hearing by the word of God
But men can refuse to listen. That is not God's fault, it is the man's fault.
Rom 10:18 But I say, Have they not heard? Yes verily, their sound went into all the earth, and their words unto the ends of the world.
19 But I say, Did not Israel know? First Moses saith, I will provoke you to jealousy by them that are no people, and by a foolish nation I will anger you.
20 But Esaias is very bold, and saith, I was found of them that sought me not; I was made manifest unto them that asked not after me.
21 But to Israel he saith, All day long I have stretched forth my hands unto a disobedient and gainsaying people.
Paul here is speaking of the Jews. God had preached to them for thousands of years through his prophets. They heard God's word but disregarded it. So God has gone to the Gentiles to provoke the Jews to jealousy. The Jews had always considered themselves the elect and chosen, now God is going to the heathen that the Jew despised. They are provoked to jealousy.
Notice in verse 21 that God had stretched out his hands all the day long to Israel, but they refused to come.
God offers salvation to all men, but you must respond and come to Christ when he calls. This is shown a multitude of times in scripture.
John 5:40 And ye will not come to me, that ye might have life.
Matt 22:2 The kingdom of heaven is like unto a certain king, which made a marriage for his son,
3 And sent forth his servants to call them that were bidden to the wedding: and they would not come.
Luke 7:32 They are like unto children sitting in the marketplace, and calling one to another, and saying, We have piped unto you, and ye have not danced; we have mourned to you, and ye have not wept.
I would hardly say God loses when a man will not come to Christ, it is the man that loses, he loses his soul forever.
Mark 8:36 For what shall it profit a man, if he shall gain the whole world, and lose his own soul?
God does not impose faith on a man as Calvinism teaches. He offers salvation to every man, but every man is responsible to respond to God of his own free will. This is shown over and over again in scripture.