Like I said, sometimes stories start off great as the reader is submersed into an epic, violent battle. However, I don’t particularly like those introductions over a girl who is just getting fed up working in the king’s kitchen with no thanks

Both examples have conflict. It's confusing because in day to day life, "conflict" almost always means people fighting. "There's been some conflict" is often a nicer way to say "Jim and Ted now hate each other."

Dramatic conflict only sometimes means people fighting. There are all of those types of conflict from school: Man vs. God, Man vs. Nature, Man vs. Man (fighting, though not always) Man vs. Himself. Two people on a date that's going well have a ton of dramatic conflict: they're nervous but trying to hide it, they're trying to impress the other person, suss the other person out. There's a lot going on dramatically, even though they're getting along swimmingly.

Pretty much any time a character isn't completely content, there's some kind of dramatic conflict. That kitchen girl getting fed up is in conflict with her station in life, with her boss, maybe the king. Harry Potter is in conflict with his awful foster family, and more broadly, this mundane world he doesn't belong in. Something needs to change.

When people usually complain in critiques that a first chapter has "no conflict," that "something" that needs to change usually isn't clear enough. It could be that there's too much description, or dialogue that doesn't go anywhere. Or, the author chose to open on a normal day, but didn't seed enough discontent into it to give an idea of where the story will go. It seems too stagnant.