Based on the original post. Sounds like fighter class with Soldier background. Done.
History covers all the military training. Survival covers all the survival training. The fact that they have the Soldier background covers everything else.
5E is based on the old school style of play where a character's background and narrative means something and it is not necessary to apply a mechanical rule to every little aspect of a character.
The player and DM should reach an agreement that the Soldier background grants the level of competence it would logically expect. If you want to look to old school you need look no further than the Background.
Backgrounds in 5E are one of the most old school elements of the game. They, literally, let you make a character that has a scope beyond the pure mechanical. If you only look at Backgrounds only in terms of their mechanics (skill picks, etc) you are doing it wrong.
The character's background is a literal narrative background that provides all the elements that would imply.
Again:
Everybody has backgrounds! That's the default, the baseline. The fact that some classes pile stuff on top while others DON'T is a problem!
Skill checks are also the baseline. Everybody gets to do them, but some classes have ways to mitigate the effect of randomness on the result. Interesting crunchy ways. The Fighter doesn't. That is also a problem.
Furthermore, I'm sorry, but I can't accept handwaving mechanical issues with some "
DM may I" principle like 'backstory' because all games are different.
When I joined a game that was underway I eventually had a chance to change my character and I went out of my way to pick the Hermit background and integrate its 'discovery' feature into the lore that had been developed for the game so far. My DM never did anything with it. Ever. All it did for me was give me a useless Religion proficiency... so excuse me for being dubious of this kind of 'patch'.
I think here is where there is a gap that we can't cover.
I say that D&D supports 1st level characters as someone who is both trained/experienced in their class as well as the "blacksmith with a hammer" or others who push through with natural aptitude, talent and the like. My understanding of your position is the rules only support the former, that there must be some direct training or experience in your class to reach 1st level.
I think we both have honest, strongly held beliefs, and feel that the rules say different things on this in different places.
We can agree to disagree. Alternately, if you're interested we an put up a poll to see what others think - if that's of value.
Anyway, thanks for a civil disagreement, even when we've both been passionate.
I don't think D&D doesn't support it, but I would argue that the default fluff,
which in turns informs the design of the mechanics, is not that. It doesn't meant that it's not supported, only that when building, say a new subclass, you can't forget the default fluff. Fluff is mutable in your own game but I think a solid basic concept need to exist for the classes when designing them.
Oofta's idea about the Blacksmith who then only uses hammers as a Fighter is pretty neat. I think that sort of integration is probably key to transition from 'no class' to 'level 1'.
I actually think a poll would be interesting to see what everybody interprets as the basic fluff. Maybe specifically just the fighter?
In any case, nothing says your character can't receive class training WHILE they are a farmer or a blacksmith or whatever day job they have. Rather, it seems to be expected in some of the more obvious class+background combinations (like Acolyte + Cleric/Paladin, Soldier + Fighter, Criminal + Rogue, etc.). The idea is that you have a bunch of proficiency, skills and abilities at level 1 and those don't come out of nowhere just because your village was razed by goblins last week. Heck, maybe you've been level 1 for a long while and only now just decided to apply these skills to adventuring.
And as for the all weapons training thing, it's called out in the class description again:
Fighters learn the basics of all combat styles. Every fighter can swing an axe, fence with a rapier, wield a longsword or a greatsword, use a bow, and even trap foes in a net with some degree of skill. Likewise, a fighter is adept with shields and every form of armor. Beyond that basic degree of familiarity, each fighter specializes in a certain style of combat. Some concentrate on archery, some on fighting with two weapons at once, and some on augmenting their martial skills with magic. This combination of broad general ability and extensive specialization makes fighters superior combatants on battlefields and in dungeons alike.