Yes, the Multiverse does exist in the MCU and it is stated as such in Doctor Strange as you mention.
The Ancient One: Learning of an infinite multiverse included learning of infinite dangers. And if I told you everything else that you don’t already know, you’d run from here in terror.
It is worth noting though that there are other mentions of the Multiverse in Dcotor Strange, however, most of them appear to talk about the other dimensions rather than other universes. And so these mentions of the Multiverse are not actually talking about the Multiverse itself.
The Ancient One: The language of the mystic arts is as old as civilization. The sorcerers of antiquity called the use of this language "spells". But if that word offends your modern sensibilities, you can call it "program". The source code that shapes reality. We harness energy drawn from other dimensions of the multiverse, to cast spells, conjure shields and weapons to make magic.
Whilst we're on the note of false positives we should explore some things like the Multiverse but aren't actually it:
Dimensions - as previously mentioned different dimensions, Astral, dark, etc., aren't actually different universes or part of the Multiverse and these are what we see throughout Doctor Strange.
Alternate timelines - A major plot of Avengers: Endgame is the Time Heist which creates different timelines. These alternate timelines can be created and erased by removing something from the "past" or putting it back but these aren't the Multiverse.
Mysterio - In Spider-Man: Far From Home Mysterio tells everyone he is from Earth, just not ours. He even gives the Earth's numbers , 833 for his and 616 for ours. However, he was lying and it was all an elaborate story and so this isn't the Multiverse and the numbers weren't real.
The Nine Realms - These are the Realms, Asgard, Midgard, etc., and aren't the Multiverse.
We have no current further confirmation of a Multiverse as far as I am aware in the MCU. However, it is important to note that the Doctor Strange squeal is to be titled Doctor Strange in the Multiverse of Madness which would indicate that yes the Multiverse does exist in the MCU. However, until the film is out we do not know for sure.
From an out of universe perspective it is of course worth noting that the MCU is part of the "normal" Marvel Multiverse with it being listed as Earth-199999 and the main comics continuity is Earth-616. It's just that currently no other universe has interacted with the MCU yet.