It is easy to get confused. There are two points of view.
The simplest is the reference frame of the in falling mass. Let's call that an in falling observer. The observer falls through the event horizon in a finite, pretty fast,period of observer time. Inside, he/she cannot communicate with the inside, but it had added to the mass of the BH.
The reference frame of an observer outside and far enough to not be much affected by the BH gravity, is that indeed it takes that particle an increasingly large amount of time to reach the horizon. In fact, in a relatively quick amount of time that outside observer can not detect light from the in falling particle (or unfortunate person). It actually happens pretty fast also; the first detected collapse of two BHs in 2015 fro LIGO had the two BHs do about 5 or 10 revolutions around each other and merge into 1 in period of about 1/4 second (of course they approached each other before that etc, we just saw the last few seconds including the final merge. We can't tell if it formed a joint horizon after merging, or something so close to it that what we measure and see (through the gravitational radiation emitted), looks just like the horizon.
This wiki article shows the merging process as a simulation. Also a NASA depiction. It's very quick. They are. Both simulations from the parameters measured in the gravitational waves detected during the merger
For a particle falling in the explanation would be that it gets so close to the horizon, maybe a few wavelengths from it, that it is as though it did get into the horizon. Some people say that what the apparent BHs have are really apparent horizons, they act like them but from an outside observer point of view they never quite form. But they get close enough that for all measurements and purposes it looks like they are.
So, you can think of the BH as having formed, practically, and treat it like one. The idea of apparent horizons to explain what different observers might see or experience is not a brand new thing, and in fact there are slightly different definitions and calculations (there's something called dynamic horizons, for instance).
So, that time dilation that an observer outside the BH, and somewhat away from its gravity, sees, that time passes slower for events close outside the BH horizon, and it slows down infinitely as it approaches the horizon, is just an observer dependent observation. For all physics, astronomy and such purposes you can treat them as Though the horizon formed.
Keep in mind that although general relativity says that nothing out of the ordinary happens at the horizon ('no drama'), a quantum gravity treatment may actually make the horizon a more active quantum object. Recently Hawking has published that 'there are no black holes'. He and colleagues have published in 2016 an article that shows some additional properties that BH horizons should have, basically additional conserved quantities they called 'soft hair'. Hawking is driven by a different possible paradox, that mass and information disappears behind the horizon, and eventually evaporates (yes, BHs evaporate, just very slowly, shown by Hawking). This would violate the law of conservation of information in quantum theory, and he's looking for the resolution of that apparent paradox. Other people are too.
There are other answers in this physics stack exchange for this question or similar. I'm trying to make sure it's understood that it is not really a significant issue. Unless you have somebody go very close to the BH, time will go much slower for them, as it did in the movie Interstellar, compared to the people back home. But for those people near the horizon, time seems to pass normally. For the BHs, they merged.