My thinking: Anarchists want to forbid the existence of the State.
This can be misleading, because Anarchism isn't so much about "the state", but about being anti-authoritarian, anti-hierarchical and against any relations that are characterized by the domination of one over another.
So as long as "the state" is characterized by one "rule making and enforcing"-agency that is independent of the people to whom the rules apply and to whom they are applied, this is a social hierarchy and a power relation that is incompatible with anarchism.
However it could at least theoretically be possible for a group to make their own rules directly. So it's not an authority that dictates but it's the free expression of the people themselves that is the foundation of these rules.
And ideally because the people make the rules themselves and are in the position to question and reformulate the rules themselves (in cooperation with the rest), they are more likely to accept the rules themselves.
So at least in theory you'd have not as much need for an enforcing agency, as you would have if the creation of these rules already goes against the will of the people to whom they apply. Likewise if the people agree with these rules they are also theoretically more likely to have a vested interest in them, unlike if it is literally none of their business.
So it's the other way around, you don't really need a large dedicated organization that enforces rules if people agree with those rules, you need that if they don't agree with the rules and feel that it's more effective to break and bend them than to report problems with the rules.
So as long as it is about individual rule breaking and small groups, spontaneous organization of society could probably do the detective work of gathering evidence, reconstructing the situation and narrowing done the problem and negotiating a solution. You could have people who do that professionally and with a transparent work process but that part is rather uncontroversial.
However, in a society with no state, someone can achieve such a predominance over their peers that they can forbid anyone else from the use of violence, in effect founding a state. (This can happen for example because this person has forced everyone else under their rule with through violence).
And how exactly do you plan to do that? Like do you think you could go to town square and say "I am now your tyrannic overlord" and people will go "YEAH!!". No the most likely response is "GTFO!". And if you go there with a gun, people will probably run away and come back better organized and with much more guns... Individually you'd be outnumbered so even if you outgun them you'd still be at an extraordinary disadvantage. Even without guns all they'd need to do is surround you with shields and wait. Rather sooner than later you'll run out of supplies and have to give up.
And if you plan to go there with a group, what is it that you've got to offer to them? Like primarily you're taking away their freedom and agency and demand their loyalty and obedience to you, so you're making demands, rather than providing reasons to follow you. Like this works in situations that are already fucked up and where you're discriminated against and have the hope that you could do better than how it's currently done. Where you're hopelessness and lack of agency over your life makes violence become a viable option for change.
But if you have better options for change (those that are less likely to get you killed in the process), are able to partake in your own governance and have much safer ways of change than violence then this is a much less compelling narrative.
So your narrative would likely have to be one of domination and enslavement where you establish yourself and your peers as an upper class. However that necessitates the cooperation of the underclass who'd again outnumber and outgun you. And pretty much by default, because the upper class has to be "elite" (selected), not even necessarily in terms of skills but in the sense of small numbers. Or how do you plan for such a society to work?
Like they'd still have to span up an economy. Like people have to produce food, health care, goods and services, part of which has to go to themselves in order to keep up the economy and only a fraction of it can be extracted by you. So pretty much by definition the productive members of society would make up a much larger faction of the population who would perpetually see you as "the enemy". Sure you can keep them dumb and powerless, but your economic output will be accordingly... So you'd either end up serving them or find your head on a pike, either by the people whom you exploit or by one of your fellow exploiters who wants a bigger share of it.
So unless you can provide for yourself all by yourself while having weaponry to keep the entire world in check your concept fails due to the basic material reality. It's fundamentally unstable and temporary almost by definition and the threat of a violent death makes it not very compelling if you have options.
So what is it that you'd actually be able to offer them as a future insurgence against the system? Like even if they win, the majority of the people following an exploiter still end up being exploited. Like the average soldier and mercenary isn't usually much better off than the peasant that they steal from, maybe even worse off actually.
So I think you underestimate how hard it is to "take power". Mind you Anarchism isn't a "power vacuum" as people confusing it with chaos like to claim, but it's an equal distribution of power. So if you try to seize power, you'd take it away from other places and thus immediately make a lot of enemies.
And coming back to your question, there doesn't even had to be a direct contradiction in terms of having a monopoly of violence of the community. Like what if you'd say that the executive power comes down to the community, to judge, disarm and capture and so on. With the usual exceptions of immediate self-defense and assistance in emergency situation. So you'd have a group meeting decide how to organize and do it.
I mean the original idea of a militia is still suitable, so an ad hoc military comprised of the citizens themselves.
The crucial question isn't the existence of such an organization of people but how it's organized and how power is distributed in it. So is it an independent agency that exerts power over other people or are the people themselves exercising their power in mutual agreement with other people?