Did the Jews that lived before Christ go to Heaven?

Some of them, depending on their works.  Every single one of God's human children shall have a fair chance to learn the gospel of Jesus Christ (1 Peter 3:18-20; 4:6) and benefit from it (1 Cor. 15:29).  Of course, evil works lead to lesser rewards than heaven.  St. Paul wrote of three glorious resurrections and their appropriate awards.

The Bible declares in Ephesians 4 and in 1 Peter 3

that after Jesus was crucified He went to those who have died before and gave them the opportunity to accept and believe in the Son of God.

Ephesians 4:8 “Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men.”

Ephesians 4:9 “(Now that he ascended, what is it but that he also descended first into the lower parts of the earth?”

1 Peter 3:18 “For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit:”

1 Peter 3:19 “By which also he went and preached unto the spirits in prison;”

Some did.....Those that had faith in God that the Messiah would eventually come and tried to keep the law.

Jesus gave us an example in the parable of the Rich Man and Lazarus.

The Rich Man went to Sheol (awaiting judgment and hell) and Lazarus' soul went to be with God in heaven.

There's no immediate admittance to heaven, after death there is silence.

Until the trumpet sounds

Throughout the Scriptures, we see many examples of men of faith who were deeply moved by holy spirit; yet they did not have the hope of living in heaven.

 John the Baptist was one such person. Jesus highly praised him but stated that John would not be included in the heavenly Kingdom.

 David was likewise moved by holy spirit. 1 Sam. 16:13

 He was a man of great spiritual depth and was even inspired to write sections of the Bible. Still, at Pentecost, Peter said of David that he “did not ascend to the heavens.” Acts 2:34

 Holy spirit worked mightily in such ones, but it did not give them the special witness that they had been selected for heavenly life.

 That did not mean that they were in some way unworthy or deficient. It simply meant that Jehovah would resurrect them to life on a paradise earth.

(Psalm 37:29) The righteous will possess the earth, And they will live forever on it.

Millions had died before Jesus, this is what he said: (John 3:13) Moreover, no man has ascended into heaven but the one who descended from heaven, the Son of man.

Not one person according to Jesus that had died had gone to heaven, as Jesus said, they are asleep waiting for the resurrection.

Jews believe that everyone (including gentiles) goes to heaven.

Christians will have a certain kind of punishment in heaven.  They will forever know that their beliefs were wrong.

Heaven doesn't happen until the day of judgment, so I think you're asking if it was possible for an ancient Jew (and even Gentile) to be saved where they would go to heaven.  And the answer is yes.  Below are some of those who hopefully you'll meet some day in heaven.

Heb 11:32  And what more shall I say? For time would fail me to tell of Gideon, Barak, Samson, Jephthah, of David and Samuel and the prophets— 

Heb 11:33  who through faith conquered kingdoms, enforced justice, obtained promises, stopped the mouths of lions, 

Heb 11:34  quenched the power of fire, escaped the edge of the sword, were made strong out of weakness, became mighty in war, put foreign armies to flight. 

The Bible teaches that no one went to heaven before Jesus Christ.

Hebrews 9:15 tells it if those Jews are among "those who are called" (faithful).