"Unfortunately, due to time dilation the time for mass to fall into the event horizon becomes infinite, so that nothing can cross the horizon within in the life time of the universe."
This can not be understood as any objective statement about coordinate-independent physical realities, since it's only true in certain coordinates like Schwarzschild coordinates. In general relativity it's the geometry of spacetime, defined by the proper time along arbitrary timelike curves and the proper distance along arbitrary spacelike curves, that's fundamental and coordinate-invariant. To elaborate on this a little, if you have two coordinate systems on the same patch of spacetime with a coordinate transformation between them, then if you describe a curve (a one-dimensional physical path through spacetime, which in the case of timelike curves could be some slower-than-light particle's world line) in terms of one set of coordinates, you can use the coordinate transformation to describe the same curve in the other set of coordinates. Then you can express the metric in terms of each coordinate system, and use it to calculate the proper time or proper distance along the curve (assuming it's timelike or spacelike rather than lightlike), and both should give the same answer, which is why proper time/proper distance is considered more "physical" and objective than any coordinate-dependent measurement.
When people talk about things taking an infinite time to reach the horizon, they aren't talking about the falling particle's own proper time, but rather about the coordinate time in some coordinate system like Schwarzschild coordinates. But even in these coordinates, you can show that the particle's own proper time approaches some finite value T in the limit as coordinate time goes to infinity. It's possible to construct other coordinate systems where the same particle crosses the horizon in finite coordinate time, and these coordinates will agree that the particle's own proper time reaches T at the moment of the crossing. One example is ingoing Eddington-Finkelstein coordinates, graphed below in a diagram from this page (the event horizon is the vertical line which has the label r=2m at the bottom):
Another example is Kruskal-Szekeres coordinates; shown below is a diagram from the textbook Gravitation by Misner/Thorne/Wheeler, showing the surface of a collapsing star (the boundary of the gray region) graphed in both Schwarzschild coordinates (which has the weird property that inside the horizon, the collapsing surface is actually moving backwards in time relative to the time coordinate) and Kruskal-Szekers coordinates (where the surface crosses the horizon, the dotted line marked r=2M, at a finite coordinate time and then continues moving forward in coordinate time until reaching the singularity, whose coordinate position is marked by the black sawtooth hyperbola):
Note that the Kruskal-Szekeres diagram also shows what curves of constant Schwarzschild position coordinate (the hyperbolas labeled r=2.5M, r=3M etc.) and constant Schwarzschild time coordinate (the straight lines labeled t=35.1M, t=44.3M, t=45.4M etc.) look like when transformed into Kruskal-Szekeres coordinates.
Another point is that this kind of issue can also crop up in the flat spacetime of special relativity--for example, in the non-inertial coordinate system known as Rindler coordinates in which a group of observers with constant proper acceleration are represented as being at rest, there is a boundary called the Rindler horizon which the accelerating observers can never see beyond, and any particle moving towards it will take an infinite coordinate time to reach it in Rindler coordinates. But in an inertial coordinate system, the same particle crosses the Rindler horizon in finite coordinate time. Drawn in the coordinates of an inertial frame, the Rindler horizon is a lightlike boundary, which would be the edge of some future light cone; and the accelerating observers, who in Rindler coordinates have a fixed coordinate position, would in the inertial frame have worldlines that look like hyperbolas which get closer and closer to the Rindler horizon but never quite reach it. The diagram below shows how things look in the inertial frame, with the Rindler horizon represented as the diagonal dotted line and the accelerating observers (or equivalently, the lines of constant Rindler position coordinate) represented as black curves, and gray :
Note that these curves of constant Rindler position and time coordinate, when transformed into inertial coordinates, look just the same as the curves of constant Schwarzschild position and time coordinate when transformed into Kruskal-Szekeres coordinates. So conceptually it may be a useful analogy to think "Kruskal-Szekeres coordinates are to Schwarzschild coordinates as Inertial coordinates are to Rindler coordinates".