As someone else said, anything is possible with God. Reincarnation is not only possible, it is universal - this is God’s way of perfecting an imperfect human by making him take multiple lives and letting him grow and develop with each step.
Remembering all lives for the human brain would be too burdensome, but the soul remembers all lives and all lessons learned. There are many levels of Gods. I doubt if the fate of an individual human is managed by anyone higher than the God of the earth (the next level would be the solar God), so doubtful if the universal God like Brahman would be involved in the details of your life(although he does care what happens to you).
After death, you don’t immediately reincarnate. You spend some time in purgatory and heaven between lives before being reborn ( a sort of rest period). Karma determines what kind of life you will have next. You can read
www.afterdeath.info if you are interested.