Jesus Christ and his mother Mary were both said to have been born “without sin.” Does that really mean, that both chose mission lives, to incarnate for the upliftment of humanity and that being “without sin,” reflects that neither had a karmic backlog of trauma that required healing?

This is the best interpretation of that designation, that there was no baggage, so to speak, no liabilities or karmic penalties coming due that needed to be repaid. In which case they might well falter in the current life mission or have distractions and periods of ineffectiveness while they were in a sense having to work through personal issues that would be, at a minimum, a distraction, and, at worst, derail their ongoing mission for a time. This is something that befalls almost every human, that there will be a lot of karma to be reckoned with. It is simply the nature of existence that the Law of Karma will catch up to a person during each incarnation and bring around to them challenges to be overcome that were left undone in prior go-rounds. Some have more work to do than others. Most people who spend lives suffering and seemingly on the sidelines, through poverty, chronic health impairment, disabilities, and other major issues rendering them unable to care for themselves or to be effective and self-sustaining in life, are actually working through serious karmic issues. And their lives will, in the end, have great meaning from having done that, but it makes them ineffective as a spokesperson and advocate for divine truth to accomplish such a mission life, as they will hardly be a good example to others to emulate. Those who see the deeper truth, that they have, in all likelihood, already served, and possibly in many, many lifetimes, and have been wounded repeatedly and are now having to deal with the consequences of victimization in many cases, will see that it is no reflection of their worth as a soul-based being, but only a dilemma of the moment. And, in a sense, their life is a consequence of wounding very much akin to the wounded combat veteran who is bestowed a purple heart and perhaps other medals for courage and resourcefulness through their leadership during extremely stressful circumstances on the battlefield. That is an apt description of what all humans are going through with their lifetimes—they are in a contest for survival with interlopers intent on destroying their world, so in that sense all are walking wounded. These exalted figures you ask about had particularly important mission lives and were in a more pristine state of being to facilitate their mission by having all karma set aside and held in abeyance so they were, in effect, blessed with extra support.