Submissions for these types of contests, and even some news agencies, require photos to be submitted as straight-from-camera JPEG files, not as exports of RAW images. This is usually enough to satisfy the submission requirements.
Most of the time, people trying to skirt such rules by faking EXIF data, tend to make a mistake somewhere, that is a tell-tale clue of manipulation. Often those clues are discrepancies in the various time/date stamps in the EXIF data and/or the filesystem metadata. Sometimes there are extra EXIF fields modified or added by their manipulation tool, that they weren't aware of.
To the point that even straight-out-of-camera JPEGs are manipulated by "decisions" in the camera's RAW processing algorithms, that ignores intent: a CPU or camera has no intent or goal; it is merely a complex machine following its programming. Only a person has intent, so implicit in the requirements for your contest are "no intentional edits" to be made.
But in a strict sense, there is no technical way to be absolutely sure an image wasn't manipulated. Because at some point along the way, we're out of the realm of technology, and into the realm of trust.
For smaller competitions, the stakes aren't worth it to ensure a high degree of trust. That is, the contest generally trusts (but attempts to verify) submissions were made according to the rules. But they're not going to employ expensive time-consuming techniques to try to disprove the trust. They will use simple, point-and-click -style tools to pass a "good enough" test. That's all they can do. As the stakes of the contest increase (such as substantial monetary rewards, etc.), the techniques and tools to spot alterations can be more sophisticated and more expensive.
For some news agencies, they actually extend the trust even quicker that submitters don't alter their images. This is because the photojournalists have a reputation to stake (as do the news agencies themselves), coupled with contractual submission agreements. Those agreements are backed with the possibility of termination or severance of relationship if undisclosed manipulations were made. See What are the editing restrictions for sports/photo journalism?
For other purposes where image integrity is absolutely important, knowing that technological means cannot guarantee image integrity, the trust is placed in processes and procedures ensuring the chain of custody, file handling, etc., is maintained, so that the opportunity to alter the image is reduced or eliminated. Things such as file checksumming, append-only data stores (i.e., blockchains), can certainly help, but they are not guaranteed to ensure unmanipulated data if there is no knowledge of the chain of custody of the data before those tools were employed.