The F15, the F16 and the F22 have the best climb rates. Whether or not they can accelerate vertically is another matter. Maybe yes, briefly, but it’s not like you think. Your thrust is not only fighting the weight, it’s fighting the drag. And the drag goes up with speed and the thrust goes down with altitude and it gets pretty complicated, pretty quickly. Time to climb records aren’t set by climbing at 90° anyway.
This is the F15 they used to set the World records:
https://www.wearethemighty.com/mighty-history/f15-streak-eagle-flight-records/