>>54011250First of all, Arven is definitely older than 13-14, he's got sideburns so he's probably around 16.
Secondly, the professor worked on the time machine for a long, long time - probably their whole life.
We know that they were obsessed with the Scarlet/Violet Book since they were a child, and they were one of the best students at the Academy, if not the best. Our school systems don't really apply to the world of Pokémon so who knows when they graduated, but Clavell told us that they've been researching like crazy even before they left the Academy (his office used to be their lab). Point is, they might've researched the time machine shit the whole time, it could've easily been 20 years. Plus, don't forget they were an extreme workaholic, they literally neglected their child for most of his life.
We know that Clavell worked with the professor for Area Zero related research a long time ago, and when he learns about the Paradox Pokémon in Paldea he says something like "[Professor], don't tell me you really did it...?" That and the journal confirms that the time machine, or at least some sort of technology that (allegedly) retrieved Pokémon from another time, has been working since around the time Arven was born.
So your argument that they didn't have enough time really doesn't hold up. Also, the Pokémon world is a lot more technologically advanced than the real world.
Honestly, the better question is what else they were researching. The Tera Orb is obviously one thing they worked on. The prototype was done before Arven was born and was made commercially available 10 years ago, which also seems to be the point where they put more into their time machine research. It kinda seems a like they mostly did that to get more funding, since the backers wanted something people could actually use and weren't interested in the time machine stuff.
Maybe that one anon is right and Terapagos has terraforming powers, which the prof might've wanted to make their "paradise" real
