To Aurora, mechanically yes, in the hard game system, that's accurate enough, but what I'll ask you to remember is that there have been times during which the weave was missing, dead or unstable, and other means of utilising magic in the world were found, tenuous and dangerous though thy were. I'll note again, Abeir, where there is no weave, still has spellcasters - though they are fewer and the process is more taxing and dangerous for a variety of reasons.

In general, without the weave, mortals cannot tap magical power - but there are always exceptions to this general rule.

I linked the page with information on these exceptions - I'd encourage you to take a read at your leisure, but the core of it is here - sourced from the Forgotten Realms Campaign Guide and Magic of Faerun primarily

Quote
Mortal beings were unable to directly use or shape raw magic—it was locked away in matter and almost inaccessible to them. Typically, they could only access wisps of raw magic released during Weave-devastating events. Those who did attempt to harness it found it a potent but very dangerous force, easily able to obliterate them whatever their cautions. They also found that magic was less malleable than when used through the Weave, more akin to throwing out energy than to molding it into a spell with specific desired effects.

The Weave, thus, served as a barrier or gate between raw magic and the world, and as an interface between raw magic and a spellcaster's will, allowing them to tap into the refined energy of raw magic and shielding them from its injurious effects, making magic relatively controlled and relatively safe. Thus, the majority of spellcasters used the Weave to cast spells.
Varieties

Nevertheless, raw magic came in various forms that could in some way be wielded by mortals:

[...]

Spellfire, and its lesser form silver fire, [...]
Mana, also called "spell power", was a form of raw magic utilized by bloodforges and mages of the Utter East [...]
Incarnum was another form of raw magic [...]
Through the study of wild magic zones, wild mages learnt to tap into raw magic independent of location, but their spells always included elements of randomness. [...]
All spellcasters on Toril who learned (or relearned) how to use magic after the Wailing Years and until the full restoration of the Weave in 1487 DR, learned how to use raw magic to cast their spells.
As there was No Weave on Abeir, raw magic was the only way to use magic on that world. Only magic items, or beings who could produce magic on their own (such as dragons or sorcerers) were able to easily tap into raw magic, however.

Emphasis mine: Typically it worked a certain way, but saying typically means that there are atypical cases and examples.
Mortal casters found that using raw magic directly was less malleable than when used with the weave - ergo, ways were found to do so, otherwise such a comparison could not be made.
The majority of spellcasters use the weave to cast spells - ergo there exists a minority who do not need to.
Times have existed during which all spellcasters had to learn to use raw magic without the weave, because it wasn't available.
In places where no weave exists at all, only innately magical creatures - which include Sorcerers - could easily manipulate magic.

The main point is that while the general rules are true generally, there are exceptions, and the weave is not strictly essential, especially for mortal sorcerers.

Mechanically, in the 5e game system it is - but that's a system balance element, because within the base lore that doesn't quite hold true. Like I said at the top - there's more nuance to it than that.