Thanks for your question.
Some authorities put the number of years per generation as 35 on average. That would give us about 57 generations between the birth of Christ and now. If you calculate a generation as being in the neigbourhood of 40 years, then there have been about 50 generations between us and the birth of the Lord. I would say we are looking at between 50 and 60 generations.
I hope you have found this helpful.