Cookies are a key part of Analytics, so I'd push back and ask what the goal is of not having cookies. The anonymous identifiers in its cookies help Adobe keep track of the user as they go from page to page, and session to session. They are the basis for Visits and Visitors metrics, but also for any sort of persistence/attribution (if a user comes from paid search then make a purchase pages later, you want to be able to tie that purchase to that paid search campaign. Cookies are what ties that all together).
There is no built-in mechanism to disable cookies; generally, either you're tracking the user (and cookies are being set) or you're not tracking (and there are no cookies). Technically, there is a way to send data with javascript without setting cookies, by hard-coding pixels, but it's not very supported and usually results in very messy data. You could also send data through Adobe's APIs, instead of relying on javascript and cookies, but that would rely on you having collected the data yourself already, and would still require some sort of identifier for each user.
Fortunately, Adobe already primarily uses first-party cookies- see https://experienceleague.adobe.com/en/docs/core-services/interface/data-collection/cookies/overview. If you have a CNAME for tracking, then those cookies are slightly more reliable (though still limited by ITP). If you aren't using a CNAME implementation, the main cookies are still first-party, though some browsers are more likely to reject them. The only 3rd party cookie, if you have it enabled, is the demdex cookie, which in theory would help you identify visitors on different domains you have tracking on.
