If you started from scratch now could you get Caim in time or is Arcarum too time gated for that?
Depends on how literal are you being when you say from scratch. If you really mean you have nothing at all it will take a really long time of gathering slowly aquired materials but probably the biggest obstacle will be the astras, which you need 314, according to the spreadsheet on the wiki. Getting enough astras is so slow and random that you may end up getting every required item from arcarum before you have enough to finally get your evoker and, like, half for another one just as you finish your first one, which is why I ask how literally you mean from scratch. Luckily, I think earth astras are not that difficult to get, at least I have 230 after recruiting two evokers and I didn't particularly tried to go for earth, so if you mean from scratch after getting one or two evokers your workload will be a bit lighter.
You'll also have to remember to get a bunch of annoying random stuff outside of arcarum, like the items from the showdown bosses which you can only fight once per day, so start killing Vohu Manah if you don't have 100 of her infernal judge crystals, Alexiel omega animas are also a pain, bestia fruits (just buy them with cerulean stones) and don't forget the evolite, which is pretty costly, and the sunstone required to make the summon SSR too.
So I think it's maybe doable if you have a kickstart, but you must also remember that Caim's gimmick is for your grid to not have any repeated weapon so you might want to start making awhole grid just for him, which is also a pain, but at least arcarum won't get much in the way since you only need to play it once a day.