Ultimately that is correct. But anyone who is predestined to have faith in Jesus Christ will believe and be saved.
No one will be in heaven who does not believe in Jesus Christ and has not been sanctified by the Holy Spirit. Reprobates are not in heaven. The redeemed are in heaven because Christ purchased them with His life and permitted them to be acquitted of their sins.
"For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God's." -- 1 Corinthians 6:20.
You're seeing life as linear. Look at the bigger picture. At the end of our life we will each either go to heaven or hell. If we end up in hell, it is because God's justice requires retribution for each man's sins. If we end up in heaven, it is because God chose to apply Christ's righteousness to our sins and allow us to be presented to God as blameless, clothed in His blood.
From the moment of creation, God ordained what would eventually happen to every person ever born. He knew to whom He would give faith and He knew to whom He would withhold faith. And those who are not given faith do not want faith.
No one is denied faith when they desire it. We are told to ask for anything we want and Christ will provide it ("Now unto him that is able to do exceeding abundantly above all that we ask or think, according to the power that worketh in us" - Ephesians 3:20).
But the point of God's sovereignty is that anyone who desires Christ does so because God first opened their eyes and ears and first gave them a new heart with which to know the truth and be saved.
That's how amazing God's love is -- that He loved us before we loved Him; before we could earn His love...
"For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth" -- Romans 9:11
But no one can desire it unless God gives it! Reformed theology is circular logic, Dr. E. In fact, it's no logic at all.