Apparently stream-entrants are destined to attain Nibbana but what about non-stream-entrants? Are only stream-entrants destined to attain Nibbana?

I don't know whether it is possible to be destined to attain Nibbana more than 7 lives beforehand. 

Is it not possible to be destined to attain Nibbana more than 7 lives beforehand ?
Say, you wanted to lose weight and stay healthy. If you have no idea about Calories, Carbs, Fat, and Exercise - you may spend years randomly trying all types of foods, fasting, etc. - your weight going up and down endlessly. But once you get a clear idea of the science behind the body weight, you start eating healthy and exercising. Then you can draw a burn-down chart of weight by day and see how fast you're moving. At this point you can more or less precisely predict how long it will take you to reach your target weight. So it gets rather "deterministic" for you (wrong use of the word but I will go with you here). While for the people who are on a random diet based on their cravings and dislikes, the weight loss is pretty much never going to happen, because they don't have a methodical system in place that creates rational causes leading in the right direction.

Similarly, with stream entry. You understand "wrongness" (dukkha), the way it arises from conflict between "is" and "should", and the behaviors leading to conflict. You also understand "peace", the way it arises from the cessation of conflict, and the behaviors leading to no-conflict. Once you clearly see that, you can act accordingly. Once you act accordingly, it can be known that you will finish the process in finite time (seven lives being a figure of speech).

It's really simple, no need to over-complicate it.