Think what kind of God would began the entire plan of Salvation with 'He will send to Hell whom he creates for hell and to heaven him whom he creates for Heaven.' God is Creator and thus Sovereign, but if He is love he makes a way for any who will to find eternal life by His work upon the substitutional cross. The cross means nothing but an ostentacious display if those who will accept it have no choice but to accept it.
As creator and Sovereign He can create the system wherein choice can be made even as He can see from the beginning to the end. The great beauty of Love is that God so loved the world that HE GAVE His only begotten son. If no one has a choice to accept or reject His Son, what does that make of such a Gift? No gift at all, merely another willful act by a self-centered being, not acting in love but in petulance.
It is a matter of the bending of the will. Before we are saved our will was to practice sin-we never do the things of God. After we are saved God bends our will to desire and follow Him. So believers DO have a choice to follow God's will or our will. But if that will was "free" that would mean that we would ALWAYS follow God's will, would it not? But that is not the case.
Our will is to be disobedient. God puts His Spirit in us to cause us to walk in His statues and obey His ordiances. Now would you say that sounds like being puppets?