Do two commas around a clause make it non-essential?

Lumen definitely the first'n's gotta be there, don't know technicalities, but otherwise, "Besides the quicker..." can be misconstrued

The 2d don't gotta

Help

Besides, the quicker he could get to them, the quicker his problems would be solved.

Keep them all in.

I agree with PUNKEY.

Okay Cis but there's a trend away from the 2d one

Call me old fashioned.

Okay Cis ur old fashioned

Me too I guess

It depends. I was always taught to remove the clause to see if the sentence still makes sense.

In this case, it doesn't.

"besides" is the only non-essential part of this sentence. it's one of those introductory words like "however," "well," and "in addition" that when used this way always has a comma after it. in your example, the comma belongs solely to besides. it would sound a little funny but you could technically move "besides" to the middle of the sentence or the end.

I see it a bit differently. I see that the break point with a comma is a complete sentence with its noun and verb.

I could be wrong but I thought a complete sentence, if we're talking strictly, has to express a complete idea, which would mean the first clause in this sentence requires the second?

You are correct. A sentence must express a complete idea.