Hi! Sorry for the late reply, I've been busy but this ask is fascinating!
Hercules or Heracles (the Greek version of his name) is a demigod.
His mother, Alcmene, is human, while his father is Zeus. He was already part god like Perseus, Bellerophon and Achilles. Hercules was only able to ascend to godhood because he was already halfway there and while humans like Patroclus and Sappho can be possibly venerated as heroes or past ancestors, ancient Greece is very explicit on making sure that any human who ascends to godhood is a demigod, even if they are said to have a human mother and human father, like the story of Theseus whose human father was Aegeus but many myths claim it was actually Poseidon: (LINK)
So, can humans who are not already demigods ascend to godhood? No, according to the ancient Greeks, they can't.
This does not mean people didn't do extraordinary things, it's just that the ancient Greeks assumed whoever did extraordinary things was a demigod. This happened because when people accomplished something extraordinary in ancient Greece, the public considered that person to be someone who went beyond human limitation and thus considered more than human. People started suspecting a god as a possible parent.
Sometimes the person claiming to be a demigod did it for political reasons, like Alexander the Great who claimed to be the son of Zeus. Did people actually believe him? Not until he was able to prove his superhuman ability by creating one of the largest empires in human history at such a young age and in such a short time: (LINK)
Another thing I want to mention is how important ancestry was to the ancient Greeks.
Every Greek person only had one name and sometimes multiple people had the same name. So in order to differentiate between two people with the same name, their "last name" would be the name of their father, for example: "Theseus son of Aegus."
When someone didn't know who the father was, they would go by the mother's name, but if the person did something extraordinary, then people would start claiming they were the illegitimate child of a god (usually Zeus) and they would speculate and make stories about them emphasizing their status as a demigod (this is one of the reasons why there are a lot of stories about Zeus and rape. To the ancient Greeks, rape ment "going behind the father's back" even if the women wanted to be in a union with the god because to the ancient Greeks women did not have autonomy so their father's permission was very important).
Classifying a person who did the impossible as a demigod was very important to the ancient Greeks for a few reasons:
1. It would create the idea that only living demigods can do impossible things and thus disencourage "regular" humans from thinking they can also do that and thus keeping them in line for the politicians in power who ruled every aspect of their lives.
2. It cemented the idea that the gods still interact with their people and future demigods will be bestowed with their blessings and thus their hometowns would also benefit from said blessings.
3. Adding to reason number 2, it was also used for tourism.
4. It kept the honor of both women and children who didn't have a man claiming to be the head of their household and thus allowed the father of the mother to not have a shamed lineage.
5. It was especially used by kings to keep tyrants from taking over and kept civilians from rising against them for fear they would be cursed by their divine parental figure.
6. It was used to explain the unexplainable and as a way to keep people from thinking they could do something without the influence of a god and thus letting it get to their heads as we see in the cautionary tale of Bellerophon who grew impatient with his accomplishments being accredited to his father Poseidon and people assuming it was because he was a demigod and not because of his own efforts. After growing so frustrated over losing so much personal credit, he demanded a place on Olympus because of all he accomplished and was sent a gadfly by Zeus for using pegasus to force his way into Olympus and thus falling to his death after the gadfly bit pegasus who bucked Bellerophon off: (LINK)
WARNING!!!:
The idea that a human can be a god is very dangerous and one often used by toxic cults forcing their will on others. They push the narrative that someone is the reincarnation of Apollo or the child of Zeus and will use that narrative to try to force people to do things they don't want to do because a living "god" told them to do it.
People who believe they are a god are often described as having a "God Complex" (LINK). Not only is having a god complex dangerous to the person and everyone around them, but it's often associated with an extreme form of narcissism (LINK) Why are god complexes so dangerous? Every human is fallible. We make mistakes and we grow and learn from those mistakes when we admit to them. People who have god complexes usually believe they are so perfect it's impossible for them to make mistakes so they blame everyone else around them and never take responsibility for themselves. As someone who grew up with very narcissistic adults with god complexes, it's frustrating to be gaslit and blamed for things you never did. They also don't believe in consent or believe they are above needing consent because they are a god and "know better."
If you meet someone claiming to be a god
RUN!
Seriously, run. Everyone has the ability to do and create extraordinary things but people with god complexes do not understand consent or how to respect the will of others because they think they are above other humans. Although I'm not a big fan of Witchtok, here's a little jingle that helps explain more about people with god complexes. (Tw: mentions of violence) (LINK)
Demigods are best left to mythology and storytelling.
They can be very inspiring, but a living "god" is very dangerous because they force their will onto others and are not above intimidation tactics. Here is a list of people who had been worshipped as living gods in the past and this includes Hitler, so you can see why the idea of "living gods" makes me very uncomfortable: (LINK)
These Delphic Maxims address god-complexes:
11) Φρόνει θνητά: Think mortal thoughts.
141) Εὖ πάσχε ὡς θνητός: Do as well as your mortal status permits.
The way that I personally interpret these two maxims is as a reminder that humans are human with human limits. It therefore asks that we not act like a god because that's assuming we no longer see ourselves as human.
It also asks that we not assume we can think like a god because that's over simplifying the way that the gods operate by applying human morals to them when they are beyond our comprehension and know things we'll never know, so they are a lot more complex than we'll ever understand, and assuming we know is to limit the gods.
But overall the main message is to respect the will of others by not thinking you are way better because you are more god-like than they are. EVERY person has the ability to be spiritual and the ability to create in such extraordinary ways that seem almost "god-like" to others but we are still human with human limits.
I personally believe human limits are beautiful and one of the many reasons why the gods are so fascinated with us. The gods get to see what we accomplish with such fragile lives, small limits that are carried by strong wills and big hearts.
I hope this helps!