There is very limited information available to answer this questions without any ambiguity. There is an assumption that God is in heaven and paradise is also in heaven, which would be a reasonable assumption in my opinion. Is there more clear evidence?
Looking at what’s available to us;
Is God in heaven and did Jesus ascending to Heaven? - YES - for the following reasons;
1 Peter 3:22 ESV Who has gone into heaven and is at the right hand of God, with angels, authorities, and powers having been subjected to him.
Mark 16:19 ESV So then the Lord Jesus, after he had spoken to them, was taken up into heaven and sat down at the right hand of God.
Acts 7:55-56 ESV But he, full of the Holy Spirit, gazed into heaven and saw the glory of God, and Jesus standing at the right hand of God. And he said, “Behold, I see the heavens opened, and the Son of Man standing at the right hand of God.”
Ephesians 1:20 ESV That he worked in Christ when he raised him from the dead and seated him at his right hand in the heavenly places,
Acts 7:55 ESV
But he, full of the Holy Spirit, gazed into heaven and saw the glory of God, and Jesus standing at the right hand of God.
Acts 2:34 ESV
For David did not ascend into the heavens, but he himself says, “‘The Lord said to my Lord, Sit at my right hand,
is paradise in heaven - YES very likely
Jesus answered, "If you want to be perfect, go, sell your possessions and give to the poor, and you will have treasure (thesauros) in heaven. Then come, follow me." (Matthew 19:21)
Whoever has ears, let them hear what the Spirit says to the churches. To those who are victorious, I will give the right to eat from the tree of life, which is in the paradise of God. Revelation 2:7
And I took the little book out of the angel's hand, and ate it up; and it was in my mouth sweet as honey: and as soon as I had eaten it, my belly was bitter. (Revelation 10:10)
2 Corinthians 12:2-4 esv - 2 I know a man in Christ who fourteen years ago was caught up to the third heaven—whether in the body or out of the body I do not know, God knows. 3 And I know that this man was caught up into paradise—whether in the body or out of the body I do not know, God knows— 4 and he heard things that cannot be told, which man may not utter.
When did Jesus ascend to heaven after crucifixion / risen? This is problematic
Same day - Luke 23.43 - He said to the thief who defended him, “Today you will be with me in Paradise.”
Luke 24:50 - 50 When he had led them out to the vicinity of Bethany, he lifted up his hands and blessed them. 51 While he was blessing them, he left them and was taken up into heaven.
The nest day - Mark 16:9-20 19 After the Lord Jesus had spoken to them, He was taken up into heaven and sat down at the right hand of God.
Two days - John 20:17 - He said to Mary Magdelene two days later, “I have not yet ascended to the Father.”
Acts 1:3 - 3After His suffering, He presented Himself to them with many convincing proofs that He was alive. He appeared to them over a span of forty days and spoke about the kingdom of God.
Other problems in answering this question
Isaiah 53:7 - 7He was oppressed and afflicted, yet He did not open His mouth. He was led like a lamb to the slaughter, and as a sheep before her shearers is silent, so He did not open His mouth.
This can be taken as
i) He did not Object to Gods will
ii) OR he literally did not speak a word. OR
However, he did speak at his trial and he spoke on the cross. He also prayed earnestly to be saved Luke 22:44And in His anguish, He prayed more earnestly, and His sweat became like drops of blood falling to the ground & "My GOD my GOD, why have you forsaken me?" (Matthew 27:46) - see link for more detail was Jesus was Forsaken - https://hermeneutics.stackexchange.com/a/62632/33268
Based on the above Jesus did go to heaven / paradise with God – WHEN is difficult to prove.
Some other ambiguities in the gospel regarding the crucifixion - https://hermeneutics.stackexchange.com/a/62267/33268