Based on the fact that children are able to perform magic with or without a wand and with or without saying or thinking any incantation, I think it is safe to say that neither the wand nor the incantation is actually necessary, strictly speaking. The incantation doesn’t seem no be necessary even if using a wand considering that waving a wand without saying or thinking an incantation still accomplishes magic. As for whether incantations work without a wand, I don’t think we have a definitive answer on that, and I could see that being difficult to answer.

My head canon is that through much of history, wizards performed magic just like children do before attending Hogwarts. It’s mostly just instinctual and rather difficult to control. Over time, they invented various potions which could give more predictable results, but that wasn’t always super convenient since they had to be brewed ahead of time. At some point, the wand was also invented which made casting spells easier by focusing a wizard’s power, but the problem still remained that the effects could be quite unpredictable, making spell casting rather risky.

It continued on like this for a long time until the next major development that came at the time of the Romans. What they managed to do was magically bind a specific phrase to a particular magical action in such a way that uttering that phrase will (mostly) limit the effects of a spell to the intended one. These phrases became known as incantations, and naturally most of them are in Latin since that was the language of their inventors.

Most probably, this technique would still be known in the modern era but isn’t very widely used since pretty much all the useful spells already have incantations for them. It would be very difficult and probably also a secret magical governments try very hard to keep from getting into the wrong hands. Some especially great wizards like Dumbledore may have actually created new incantations of their own through this technique, but most of the time, when we hear about someone “inventing a spell” they aren’t actually magically binding a new incantation but are instead just figuring out the wording of a long forgotten incantation.

Edit: Pretty sure Voldemort also invented a new incantation because there is the one for the dark mark at the very least.