Not men, but women and children were.
It all depends on what you mean by "born again."
Does "born again" or my preferred interpretation of John 3, "born from above," mean someone who has the indwelling presence of the Holy Spirit?
If so, then no.
If you are asking if persons knew God, were empowered to obedience, experienced grace, and received eternal life, then yes.
I think we must look to the New Testament definitions of New Birth, which can easily be understood if we simply look at the condition of the New Testament believer and contrast that with the condition of the Old Testament believer.
A few things to see as different would be...
1. The redemption of transgressions as opposed to the awaiting of redemption, or forgiveness of sin which is complete (no longer requiring the substitute which was animal sacrifice).
2. The Eternal Indwelling which began with the Coming of the Comforter as opposed to the Spirit of God ministering under Old Testament standard.
3. Entrance to Heaven upon death as opposed to Sheol/Hades.
4. The fulfillment of promise as opposed to awaiting it.
When we consider if we are saved in this Age we would not say we are unless all of these are true. We can say we have benefitted from the above whereas the Old Testament Saint had not.
The New Birth, as I see it, is the event in which through faith one is Baptized with the Spirit of God, which is the reason why we are a "new creature." Formerly we were natural men, separated from God at birth, and without life. When we are indwelt by God our natural condition, that inheritance from Adam, is corrected, and we have Eternal Life based on our union with Him.
The difference between those who have eternal life and those who do not is simply a matter of those who do are indwelt in the New Covenant "reunion" of God and man. We are reconciled in this union which is a different relationship than that afforded in the Old Testament between God and men. This is why Christ states "I am the True Vine," contrasted with the former relationship which was basically through Israel. Relationship would no longer be through the Covenant of Law, but through Christ Himself.
God bless.