Did the old testament people have hope of salvation? - This is the question I will answer.
Matt 8:11 And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven.
Jesus, by telling this clarified that Abraham, Isaac and Jacob will be in the Kingdom of heaven.
The author of Hebrews makes it abundantly clear, after giving a list of old testament characters who overcame by faith, he said:
Heb 11:35 Women received their dead raised to life again: and others were tortured, not accepting deliverance; that they might obtain a better resurrection:
Heb 11:39,40 And these all, having obtained a good report through faith, received not the promise: God having provided some better thing for us, that they without us should not be made perfect.
They without us should not be made perfect - clearly means that when we obtain the reward of life, they will obtain it too.
Heb 11:13-16 These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth. For they that say such things declare plainly that they seek a country. And truly, if they had been mindful of that country from whence they came out, they might have had opportunity to have returned. But now they desire a better country, that is, an heavenly: wherefore God is not ashamed to be called their God: for he hath prepared for them a city.
God told Daniel:
Dan 12:13 But go thou thy way till the end be: for thou shalt rest, and stand in thy lot at the end of the days.
Daniel will receive his reward at the end of days, in the resurrection of the just.
Job 19:25-27 For I know that my redeemer liveth, and that he shall stand at the latter day upon the earth: And though after my skin worms destroy this body, yet in my flesh shall I see God: Whom I shall see for myself, and mine eyes shall behold, and not another; though my reins be consumed within me.
Ps 17:15 As for me, I will behold thy face in righteousness: I shall be satisfied, when I awake, with thy likeness.
When I awake with Thy likeness - with God's likeness. This happens at resurrection.
1John 3:2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
Forgiveness of sins were promised to the people of the Old Testament as surely as it is promised to the New Testament people
Isa 1:18 Come now, and let us reason together, saith the LORD: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool.
Ps 51:1,2 To the chief Musician, A Psalm of David, when Nathan the prophet came unto him, after he had gone in to Bathsheba. Have mercy upon me, O God, according to thy lovingkindness: according unto the multitude of thy tender mercies blot out my transgressions. Wash me thoroughly from mine iniquity, and cleanse me from my sin.
Ps 51:7-12 Purge me with hyssop, and I shall be clean: wash me, and I shall be whiter than snow. Make me to hear joy and gladness; that the bones which thou hast broken may rejoice. Hide thy face from my sins, and blot out all mine iniquities. Create in me a clean heart, O God; and renew a right spirit within me. Cast me not away from thy presence; and take not thy holy spirit from me. Restore unto me the joy of thy salvation; and uphold me with thy free spirit.
Ps 32:1-6 A Psalm of David, Maschil. Blessed is he whose transgression is forgiven, whose sin is covered. Blessed is the man unto whom the LORD imputeth not iniquity, and in whose spirit there is no guile. When I kept silence, my bones waxed old through my roaring all the day long. For day and night thy hand was heavy upon me: my moisture is turned into the drought of summer. Selah. I acknowledged my sin unto thee, and mine iniquity have I not hid. I said, I will confess my transgressions unto the LORD; and thou forgavest the iniquity of my sin. Selah. For this shall every one that is godly pray unto thee in a time when thou mayest be found: surely in the floods of great waters they shall not come nigh unto him.
David said everyone who is Godly shall pray for this forgiveness of sins in acceptable time. Anyone whose sins are forgiven is just and will partake of the resurrection of the just, as given in Daniel 12:3.
P.S. I do not believe anybody goes to heaven at death. It happens at the resurrection of just except in cases where the Bible specifically says that such a person was taken by God - Examples: Enoch, Elijah.