How does one know if one is destined to attain Nibbana? (In future lives)
Traditionally, one hears it from one's teacher (Buddhist mentor). For example, my Zen master once said, pointing at me, "One day this guy will get everything. He will be Bill Gates". This is known as "the prediction".
Even without that, the teachings say, if you are committed to figure it out, however slowly, you will get there sooner or later.
This abstract idea that Nibbana is actually within reach gets concrete and personal only at pretty advanced stages. Basically, once you clearly see the mechanism of conflict/suffering and how it all works, and not just see but get some grasp of mastering unconditional "rightness", that's when you know you will get there with time.
How does one know if one is destined to attain Nibbana?
There's a type of higher knowledge called "Reviewing Knowledge"/PaccavekkhanaNana, which is developed by one who has destroyed all defilements thru the cultivation of Sila/Samadhi/Panna (virtue/meditation/wisdom):
"As the trainee trains along the straight path, the knowledge of destruction arises first, immediately followed by final knowledge. Thereafter, when the fetters of existence are destroyed, for one liberated by final knowledge, the knowledge arises: “My liberation is unshakable.” ~~ AN 3.85 ~~
When you become a Sotapanna it assures enlightenment within seven lives.
"The laywoman Sujata, Ananda, through the destruction of the three fetters has become a stream-enterer, and is safe from falling into the states of misery, assured, and bound for Enlightenment.
You couldn't know prior to the unfolding of right view with regards to seeing through the illusion of self (sotapanna) and even then there's no certainty in this life. Perhaps right effort will see to that.
How do you know if you're sotapanna? Have a read of Dhamma and Discipline of the Buddha’s Own Words to proclaim Stream Entering by oneself.