The way I look at this is that it's like the weather.
There are forecasts, which say 'It is likely to rain', available in advance - not perfectly accurate but are an indication of what may happen.
Then there is the looking up at the sky, with approaching big black clouds so 'It looks like rain' - but we might be lucky.
We see cars coming the other way with their wipers on - definitely raining up ahead, but not raining with us.
Then it does start to rain, at first lightly, then heavily.
After a while, if we are out in the rain without an umbrella, we get soaked through.
However, if we have been inside doing something else, we don't see any of this, and look at the puddles on the ground 'Oh, it's been raining'.
For Covid, modelling is like the weather forecast. Other countries are the cars coming the other way. Cases are like the rain falling on us, hospitalisations like getting soaked throughand deaths like the puddles. Just because we haven't seen the hospitalisations yet doesn't mean that we're not going to see them - it's just that it takes a while to get to that stage.