I have the impression that if a Japanese uses the term 神様, they refer to an omnipotent deity very similar to the Abrahamic god. According to my (very limited) knowledge of Shinto and Buddhism, there is no such equivalent in these beliefs, correct me if I'm wrong! So I was wondering if that term or the connection of the term with the concept emerged with Japan getting in contact with Christianity or if it has a different origin?
Any meaning that refers to any singular omnipotent being is likely from Christianity. Japanese culture has been, so far as we can tell, polytheistic, syncretic, and animistic for the entirety of the historical record, and for as much of prehistory as we can reconstruct from archaeology and other sources. *Anything* can have a kami, as the inherent force or "that-ness" of the thing. As a consequence of this idea, kami are generally not regarded as omnipotent.
Not just one
Even with regard to Christianity, from every Japanese person I've talked to about this, the general attitude is not "the Christian God is the one and only, and I forsake all belief in any other god or spiritual force", but rather, "okay, I'll cover my bases in case Christianity turns out to be right, and try praying to this Christian god as well."
(This may explain why the Mormons seem to make such headway in Japan when kids on their mission report so many converts. Once the annual tithe rolls around, a lot of these new Mormons apparently decide it's a bit too expensive, perhaps especially so when compared to the handfuls of loose change that seem to suffice for the local Shinto shrines.)
This "both / and" idea, rather than the "either / or" dichotomy imposed by the Abrahamic religions, is a large part of the modern Japanese approach to religion in the culture at large. After birth, one is blessed at a Shinto shrine. Later, one gets married in a Christian church. And at death, one has a service and a memorial at a Buddhist temple. It's quite practical, in its way.
The Japanese term 神様【かみさま】 consists of two parts: 1) 神【かみ】, referring to a "god" or "deity" or even "spirit" in certain contexts, and 2) 様【さま】, an honorific suffix. Both terms have long histories in the Japanese language, with roots tracing back to the very first long-form Japanese texts from the 700s.
Digging around in the University of Virginia's online corpus of Japanese works, a search for the term 神様 finds hits in The Tale of Genji from the early 1000s, often considered to be one of the world's first novels. ⇒ Given that this first quoted use (that I can find in a quick search; older ones might be out there) pre-dates any Christian influence on Japanese culture by roughly 500+ years, we can say pretty definitively that this term 神様【かみさま】 was not coined in response to Christianity.
⇑ As Aeon Akechi noted in the comments, I failed to notice that the Genji hits at the UVA site were for a modernized version. Searching through the digitized-but-otherwise-mostly-unaltered text available at Wikisource revealed no instances of 神様【かみさま】 or various alternative spellings.
After further research into the specific sense development of 様【さま】, I found that the honorific usage was an extension of an older meaning of "facing, direction", used later as a polite form of indirection to indicate a person, and from that we got the honorific suffix usage appearing in the 1300s. This gradually replaced older 殿【どの】, in turn from regular noun tono "lord", which sense grew from earlier "estate, mansion" to indicate the person living in such a grand house. This kind of polite indirection gradually shifting to honorific or even pronoun usage is quite common through Japanese history; for that matter, the common term anata as a basic-politeness term for "you" originally meant "that thing or person in that direction way over there".
In the oldest texts, the common honorific for kami wasn't a suffix, but rather the prefix 御【み】, and we can find lots of ancient examples of combinations like 御神【みかみ】 and 大御神【おおみかみ】. However, we don't find any instances of 神殿【かみどの】 where the 殿【どの】 is an honorific -- instead, the dono here still has the "mansion" meaning, and kamidono is a rare and now-archaic reading for modern term 神殿【しんでん】, which refers to a shrine.
I can't get a solid date on the first appearance of 神様【かみさま】. I've gone through what I think are all of the digitally-searchable texts categorized as "middle ages" (中世, roughly 1100 up through 1600) over at the Japanese Wikisource, and found no instances of any spelling of 神様【かみさま】, even unlikely alternative spellings (神様・神状・神方・神さま・神ざま・かみさま・かみざま).
Tentative (revised) conclusion on the origin of 神様【かみさま】
Considering the following:
- 神様【かみさま】 doesn't appear in any of the "middle ages" Japanese works that I've searched
- the existing 御神【みかみ】 honorific reference to kami may have been regarded as archaic, and/or too specific to local belief and likely viewed as "heathen" by the Portuguese
- 様【さま】 was likely in common use as an honorific suffix around the time that the Portuguese were actively translating Christian texts into Japanese
... it certainly seems within the realm of possibility that the specific construction 神様【かみさま】 was coined in relation to Christianity. However, I cannot find anything conclusive at this point.
Note: In modern usage, as pointed out in the comments earlier, this term can refer to any god or gods, big or small, of whatever tradition.
Please comment if the above does not address your question.