Let's try to make a realistic and practical answer without invoking extreme hypotheticals.
Let us address the three sentences in the question:
Many people advise that one should invest money in indexes like the S&P 500 because they always grow in the long term.
Any people who literally said that are fools.
There are two separate, specific, and important reasons they are fools:
- Major markets often plummet for a few decades. The example usually given is the Nikkei which went directly downwards from 40 thousand to 10 thousand for 20-30 years...

See the horror here: link
- People who talk about "long term" ignore the remarkable reality that humans die. The notion that something will be "just fine" in 30 years is an astonishingly facile comment, for a 40 or 50 year old human.
Indeed, in the Nikkei example it did in fact recover ... after right on 40 years. So, if you were 40 years old and you invested - great news! - when you are 80 years old your money has got back to precisely where it started (that's nominal money, not even considering that inflation has made it worth nothing).
Is it possible that the S&P 500 could fall to its early 1990s level? What situation could cause that?
The story of the S&P is that
- it traded around 500
- it had two ENORMOUS spikes around 2000, and then
- the overwhelming economic feature of the world is that from the 2nd of March in 2009 (Monday right?) the S&P has had a staggering, amazing, world-historic run up from around 500 to today's values .. a run-up of about 6x.

As if needed, here I indicate the run-up:

If you arrived from Mars ...
Say you arrived from Mars this afternoon. Like any alien, your only interest is trading the markets. You have to report to home base with a summary of Earth. Your summary would be:
"So, the S&P ran up 6x from Monday in 2009 through today."
That's all you'd say.
Everything else is: trivia. You wouldn't mention oil, wars, the invention of the internet, Tom Brady being the goat, or anything else. You'd just say "So, the S&P ran up 6x from Monday in 2009 through today."
So what happens next?
Whenever there's a run-up there's a pullback. End of story.
Pullbacks are usually half the runup. But whatever, it might be "merely" 30% or maybe 70%.
This means ............. you face an incredible problem.
Ouch. What's the problem?
The issue "Whenever there's a run-up there's a pullback" creates the most difficult problem in life.
You have two approaches:
Assume that the pullback is coming. Sensibly don't invest, because you could lose your money at a stroke!
Jump on, it is obviously and clearly going up, so jump on.
Two total disasters to choose from...
And there's the rub.
You're "damned if you do and damned if you don't."
With option 1: the S&P could easily double or triple again. There's absolutely no way to know "where we are" in the runup. If you miss the double, you have missed literally the one chance in your life for a double. You have completely, utterly, blown your whole life investment story.
With option 2: the pullback could start tomorrow, at, let's say, 11:25. So in 10 years folks will say "How interesting, the S&P has gone straight down since Friday Jan 22 at 11:25. Wow, if you invested your money at 11:24, you would feel really suck just now."
Both options are a complete nightmare.
Should I be afraid making a long-term investment (15-20 years and more)?
The run-up has lasted since that Monday for 11ish years now. Pullbacks are usually shorter than runups (they are more violent, faster).
Will there be a recovery after the pullback? Yes. (Just as with even the Nikkei ultra-disaster.)
When will the pullback happen? Utterly unknowable. Could be tomorrow or 10 yrs from now. It's perhaps reasonable to guess "some time" in the "coming 10 years".
So after the pullback, when will it have recovered?
There's the rub. Your question ...
Should I be afraid making a long-term investment (15-20 years and more)?
... is simply equivalent to asking "will the coming pullback-recovery of the S&P be over and done with by 20 years from now?"
If you look at the Nikkei example, "you're screwed". Conversely, you can find many other examples where the "waiting period" in major market pullbacks is more like 15 years in total.
To copy and paste for a summary:
Your question ...
Should I be afraid making a long-term investment (15-20 years and more)?
... is equivalent to asking "will the coming pullback-recovery of the S&P be over and done with by 20 years from now?"