I'm not native English and some work colleague and me were discussing about if saying human first or human-first is a correct English expression.
For example, we may promote that our company thinks of humans before machines so we might say:
It's just a sample sentence to provide an use case of human first.
Is it correct?
Thank you in advance!
No, it's not "correct" to say Human first. Certainly in any normal context it wouldn't be considered a credible "sentence". The nearest equivalent I can think of is...
...which is essentially an imperative command reduced from something like "Let women and children go first", or "Put women and children first in priority". Grammatically, the equivalent for human should probably be...
Humanity first
or
Human beings first
Note that the women and children version is idiomatically well-established, and actually means something in real-world contexts (emergencies such as a shipwrecks). In practice, OP's version is simply marketese (a marketing slogan), so it doesn't need to "mean" anything, or adhere to any grammatical principles.
It's also worth pointing out that syntactically, human is normally an adjective. It can be used as a (countable) noun, in which case in functions similarly to woman, child, person. I suppose given the way Toys R Us tramples over standard grammar and orthography, they could feasibly adopt a slogan such as "Child first". In language terms it would be "weird", but at least it might grab people's attention.
There are actually several different issues with the proposed statement which need to be addressed:
The first question that comes to mind when reading "human first" is "which human?". Is only one human being put first? If the answer is yes, then you probably need to specify more precisely which one:
"Put that human first," said the robot overlord to the executioner.
The answer is probably no, though, and you really meant to put all humans first, in which case "humans" needs to be plural here:
The angry mob shouted, "Humans first!"
No. There is no verb here, so you can't just use it by itself as a sentence. A proper sentence should say something like "Humans should come first."
It is common in some circumstances (slogans, headlines, etc) to leave verbs out of sentences when the meaning can be understood without them. This can be done for emphasis or convenience (when chanting a slogan), or to save space (when writing on signs or printing newspaper headlines). It is also sometimes done in advertising. It's important to note, however, that while this is common, it is still not grammatically correct, and should not be done in more formal contexts. A more correct way to write your text would be:
Humans should come first. We prioritize human development, because we love our job. Customer satisfaction starts with our own work happiness.
Using a period to separate the first sentence from the rest of the statement is technically OK, but since the first bit is serving as an introduction to the rest of the text, arguably a better choice here would be a colon:
Humans should come first: We prioritize human development, because we love our job. Customer satisfaction starts with our own work happiness.
Regarding "humans first" vs. "humans-first", connecting words with a hyphen changes them into an adjective (or sometimes an adverb), which means they then need to be used to describe something else:
We believe in putting humans first.
("humans" (noun) are being "put" (verb) "first" (adjective))
vs.
We have a humans-first attitude.
("humans-first" (adjective) is a modifier of "attitude" (noun))
