So did countries outside of the united states suspect "Something big is coming"?
The answer was undoubtedly yes, both because the international community of physicists had some sense of what other physicists were doing before they "disappeared" from public view and because there were both German and Russian spies in the US that were actively involved in espionage related to the Manhattan Project. The Russians were informed of the project via a British sympathizer/traitor in 1941, soon after Britain became involved.
There is some detail on individual spies at the Atomic Heritage Museum you may find interesting. This article in Smithsonian offers more detail. Finally, the Department of Energy itself maintains a history page that has good profiles on the most famous atomic spies: Klaus Fuchs, the Rosenbergs, and David Greenglass.
There are some flaired atomic historians here who can add more detail and better sources-- these are just quick, popular sources to get OP started.
There is no evidence that the Germans or the Japanese really had any indication that the US was working on atomic bomb, if that is what you are asking. I have written on the German case here — there are a few interesting data points, but all point to them not really understanding the magnitude of what the US was doing. There were also a lot of weird rumors circulating at the time, and figuring out which weird rumors were likely, and which were not, was a non-trivial issue on both sides of the war.
The Soviets knew of the bomb project, of course, through espionage. The UK knew because they were partners.
There are also cases of isolated scientists in other countries figuring that it was probable that the US was enriching uranium. But most scientists would have put long odds on the endeavor unless they knew its magnitude. In the end, the US employed something like 500,000 people total on the Manhattan Project, which is a little under 1% of the entire US civilian labor force during WWII.
I haven't seen anyone else bringing this up, but when a group of 10 senior German scientists (including Heisenberg) were held on house arrest by the British after the war all of their conversations were recorded and have been published in a number of different books. They are called the Farm Hall Transcripts if you want to read them all, but here is an excerpt from them that discusses it somewhat. The Germans knew that the Americans were trying to weaponize nuclear power, as they were trying to do it themselves, but they didn't seem to think that it was possible in the time frame of the war. So these scientists at least ended up being extremely surprised about the dropping of the atomic bomb. They actually believe that the reports couldn't have been correct when they first heard it, as they were adamant that a nuclear bomb was not feasible in such a short time frame. I'm not in a position to say whether the German government knew exactly what was going on, but at least the scientists advising them didn't think it could actually be finished.