Space (better space-time) is not like a trampoline. That's just a really poor image that is mostly used in pop-science, even by people who know better like Kip S. Thorne. I did hear him use a much better analogy once in a talk for physicists in which he compared gravity to a river:
If you want to stand still while swimming in a river (relative to the banks of the river), you have to keep swimming upstream (use your rockets...) or be anchored to something (stand on the surface of a planet). As long as you are swimming with the stream, the water doesn't exert any forces on you, but if you want to stand still relative to the banks (or swim upstream), then there will be a significant force against the flow of the water.
The analogy for a black hole then becomes a circular waterfall: you can drift all the way to the edge of the falls and keep swimming there until you are tired (your fuel runs out...) and even swim back upstream (if you brought enough fuel...), but as soon as you fall over the edge, there is no swimming back! Over the edge of the falls the world at the level of the river disappears and it's only down from there... towards the level of "the singularity", that's the bottom of the falls that will crush you.
The model is not perfect, of course (it doesn't work for orbits), but it motivates that spacetime (which is the real foundation of gravity) has a one way component: time.
Now... in reality all of this is a lot more complicated and you will have to learn general relativity, if you really want to understand the details. The good news is that the golden time of gravity research has just begun. If you decide to become a physicist, you will see absolutely amazing things in your lifetime and many may be related to research on space, time and gravity.