The problem with this approach is that even if someone had attained knowledge of previous lives, and said that they had, you would still be doubtful whether they were deluded or their experience was trustworthy.
There is another method to gain confidence in the Buddha's enlightenment, by using logical inference.
Whatever anyone says, or whatever one reads in the Pāli texts or Commentaries, it is still going to be something that will remain beyond one's personal experience until and unless one can attain psychic powers, which by all accounts is very rare these days.
One can visit any hospital or farm to see birth and death taking place on a daily basis. Most of us only rarely see either event happen in front of own eyes. Still, even if one sees birth and death frequently, it takes a leap of faith to make the connection to believe in rebirth.
If you have trouble with the doctrine, then set it aside for now, and focus on what you can know in the present life — the birth and death of your own thoughts, feelings, cravings, fears, etc., and try to understand how the arise and pass away dependent on conditions.
• • • • (Upasampadā: 24th June, 1979)