[talanum1 (OP)]

Since time goes to infinity as matter fall throwards the event horizon of a Black Hole, how will we ever be sure that matter actually falls into a Black Hole?

[evan_au]

It all depends on your frame of reference.

If you are outside the black hole, you never see an infalling spaceship cross the event horizon (but you would see it get red-shifted away to nothing in the very short time that it takes to approach the black hole).

If you are in an an infalling spaceship, you would get spaghettified at some stage:
- For stellar mass holes, you get spaghettified before you reach the event horizon
- For supermassive black holes, it is possible to cross the event horizon before tidal forces tear you apart
- But you never actually detect crossing the event horizon (it's nothing special)

Frankly, the speeds of objects falling into a black hole reach a significant fraction of c (eg c/3), so things happen on a timescale that is too short for the human visual system to grasp.