The region outside a star of mass $M$ has a certain type of curvature. That type of curvature gets stronger the deeper in it goes.
If you had a star of mass $M$ and then had a shell of mass $m$ around it, then the curvature would be of type $M+m$ outside the shell. And it would be of type $M$ inside the shell but outside the star of mass $M.$
So a big ball of gas basically is a series of shells. So the type of curvature gets smaller and smaller the deeper you go.
So long ago when our sun was a big ball of gas, spacetime outside the whole ball was of the same type as is outside the sun now, of type $M_\odot.$ But the type of curvature deeper inside was of smaller and smaller type. So the curvature where the earth is now, wasn't as large back then.
Then, as the gas collapsed, the type $M_\odot$ that was outside got to go deeper, because the type only changes when it meets energy, momentum, pressure, or stress. So eventually, that stronger type got to exist where we are, and that's how strong curvature comes about.
Now as the sun got smaller and smaller, that type $M_\odot$ curvature got to go deeper, but still only goes as far as the outer layer of the sun. And it would have to get much smaller than the sun before a black hole formed and it doesn't go that deep.
To get that deep, the same mass of the sun, $M_\odot$ would have to be concentrated very densely. So the denser you are, the farther in your outer layer can be, and the more space that larger type curvature can extend itself. And since that curvature type is stronger the deeper it goes, you get stronger curvature when you are denser. But the curvature is only stronger when you are closer.
A black hole with the same mass as the sun, would feel just as strong way out here. It's just that when you get close to the sun you aren't aren't as close to the black hole. Which means you can keep moving inwards towards the balck hole without passing into deeper layers of a weaker type of curvature.
That's what makes things strongly curved near black holes. Of course you are right that a black hole looks black solely because it is slow motion and red. And we never actually see an event horizon form if we stay outside. So its entirely theoretical unless you want to go inside.
What we see is each layer of the star we see it from back before any event horizon formed. Moving slower and looking redder. And then even slower and even redder. Never forming.
It like if you knew an employee was about to say "I quit" over the phone over a second. And you decided to record it and play the first 1/2 second of the recording over a decade and play the next 1/4 second of the recording over the next decade and then next 1/8 second of a recording over the next decade. And so on. You could claim you haven't finished hearing them say they quit. What you hear would be slower and deeper sounding and fainter. And of course your ear would stop being able to hear such deep sounds after a while.
This time dilation ends up having other consequences. That curvature of type $M$ has time tick at a different rate than the curvature of type $M+m$ outside the shell. So they disagree at the speed the matter falls. And so they disagree about how far it fell too.
So the people on the outside think it fell farther than the people on the inside do. So the shell ends up falling downwards more than it gets closer to the star. The surface of the star itself ends up farther away from the distance people when the shell contracts.
Creating space is natural when stars form. As natural as creating the curvature and the time dilation.