The Nintendo Switch is a huge success in the world, it reached 60 million units in just 3 years. Is it possible to see the Nintendo Switch come first surpassing the PS2 and Nintendo DS?

I don't see the Switch outselling the PS2 or the Nintendo DS, but I think it'll outsell the Wii. :)

Wii yes
DS no

I think there is a real possibility that it could be the best selling console of all time (and most likely the last console that has a real chance). The Switch was at roughly 55.77 million units sold as of March 2020 (3 years). I strongly believe the Switch will have another 20+ million hardware units sold this year and next (3 years in a row of 20+). So come March 2022 it will be at about 100 million units sold in 5 years (possibly more!). Then you add a couple years like the first couple (roughly 35 million in years 6 and 7) and it tail ends with roughly 20 million units to the end of it's lifecycle and it would put it right up there with the PS2.

Some reasons why the Switch will have a longer than usual lifecycle; first it has a mass handheld appeal that will carry the last few years of it's sales as more and more 3DS/DS owners migrate to the Switch. Second, Nintendo has a singular focus for the first time since 1989 (Gameboy release) and we will see that in the coming years. They are going to ride the Switch for as long as they can (as would I).

The Switch is a very unique system in that it appeals to more markets than any other system ever has. You have a huge handheld market that will be migrating to the Switch over the next 5 years as the 3DS/DS systems are being sunset. You have a mass appeal to the "casual" market. And there is a major appeal to the "hardcore" gamer's as well with some of the ports that have been accomplished (Witcher 3, Doom, Skyrim, etc). We have never really seen a system like the Switch, it will interesting to see how it influences the video game industry over the next 5 to 10 years.

EDIT: If GTA, CoD, etc ever made it to the Switch, it would be over.

Highly unlikely.

Comes down to how long they keep it active for example at the current rate it'll be at 90m plus by the end of next year which is 4 years in at that point it doesn't need record breaking years to have a chance but time on the market.

There is a chance, but it is not likely.

To sum up, here a list of past and future factors to influence the final result:
- Quarentines: there are more to come.
- Economic crysis: there is one to come, for sure.
- Nintendo creating good quality software for the console.
- PS5/XSX at a different, higher, entry price.
- Is the Ring-Fit 2 going to be even more successful than the first one?
- ... the Monster Hunter issue.
- The presence of Nintendo (Mario) in the olympic games of Tokyo 2021; how much?

So in the past we have seen Switch selling a lot due to quarentines in all the regions of the world. This is obvious because people look for a device to entertain themselfs and to calm down the children. Specially, for the parents it is more convenient to buy from Nintendo, because it is tendentially more children friendly.

The economical crysis to come should also statistically benefit the cheapest console option, rather than the more expensive new PS5/XSX. Furthermore, Nintendo could reduce the price, they definitely have a margin for it, while Microsoft and Sony not until... 2022?

Thirdly, how much longer is Nintendo going to support the Switch before releasing the successor? And during this time how many games is Nintendo going to release per year? This year 2020 is a disaster (unless they come up with something unexpected before the end of the year). Nintendos games are still great, but one would expect to have more of them, and to be more evenly spreaded throughout the year.

2020 and probably 2021, will be very good years for the Switch whatever it happens. On the other hand, to get to the 140M sold, Nintendo will also need 2022 and 2023 to be very good years, and that is the difficult thing. So I would say:
+ If the global crysis hits hard.
+ If there are still quarentine-like (recommendations for the children to go out less on certain periods) things in parts of the world on 2022 due to the third, fourth waves and mutations of the virus
+ If there is a Ring Fit 2 that is even better than Ring Fit 1 and attracts more casual people
+ If Nintendo creates MORE good games per year and spreads them evenly
+ If the console goes down in price before the public has lost the interest in it
+ If there is a new Monster Hunter in the console, or alternatively a Dragon Quest
+ If PS5 and XSX have a tough start of the generation (for whatever the reason: price or public not finding them appealing for the lack of exclusive games)
++ If he presence of Nintendo (Mario) is huge during the Olympic games, renewing the interest of the people in the console at such late stage of the consoles lifecycle

Well THEN, only then and just MAYBE, we could be thinking about crossing the 140M mark... and NDS sold 154M.

There's at best only a 5% chance of that happening. PS2 sold so well because it was the successor to the titanic PS1. And it continued to sell very well after the PS3 launched due to the PS3's high price and at times lack of software. The PS2 was $129.99 when the PS3 launched at $499.99 and $599.99. If there's even been a next generation vs. old generation price gap that large, please let me know.
The DS was a lightning in the bottle device as well. Smartphones were almost non-existent in 2004. The DS was an inexpensive portable device with a massive library and a touch screen. It was the first Nintendo device with built-in internet, and it had GBA backwards compatibility.
Switch can and likely will outsell the Wii and PS1. Anything else is a pretty tall order.

Yes.

Yep. It has a way biggest library than the DS and still has a lot to offer (the usual suspects + second pokemon generation and at least one other remake), and is 2 generations ahead as a handheld device, it still have a price cut to offer too and end its life with at least +3000 games which hasn't been achieved since the Game Boy family (which went for 15 years with 2 major revisions and 3000 games released on it)