I agree the best advice is to use backgrounds to model this. With one level of Barbarian, at the cost of being one level behind in Wizarding, you gain:
1. +6 hit points, compared to other wizards.
2. proficiency in light and med armours, OR +3 to AC from thick hide.
3. proficiency in Strength and Constitution saves.
4. proficiency in martial weapons and land mounts (and one extra skill).
5. ability to rage
Of these, 1, 2, and 3 are certainly useful for any Wizard. 4 has limited application, and 5 is functionally useless. So even though you are choosing a build that is counter-intuitive, it is workable.
Of course, someone from a Barbarian tribe does not need to be a "barbarian" in terms of class. Consider the fighter, for example (which fits the story you have described just as well; even if you have gone into a rage [as part of the story] there is no need for the character to have the rage mechanic). With one level of fighter instead, you would have:
1. +4 hit points, compared to other wizards.
2. proficiency in all armours.
3. proficiency in Strength and Constitution saves.
4. proficiency in martial weapons and land mounts (and one extra skill).
5. second wind
6. fighting style (protection, defense, or even -- to run with the theme -- GWF!)
The difference between these two (for the perspective of someone with an initial level who then chooses to become a wizard) is:
-2 hit points (relative), in exchange for heavy armour proficiency, second wind, and a fighting style.
I'd suggest that's going to serve you better long-term, and still fits your concept and your desire to have an initial non-wizard level.
(EDIT: I'm all in favour of making suboptimal builds work.

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