No different than any other plant. When you can safely pull it out and gently place into a large pot, it's good to go. Enough roots and a little moisture will prevent the rootball from falling apart during the process. If concerned, snip the cup off and it's even less concern pulling it out. Either way, loosen it a bit before pulling it out. 14+ days above ground, i'd wager. I used to use solo cups, but use smaller 2.5" pots now.. that takes 10-12days before they are ready for a bigger pot.
A great way to recognize enough root growth to warrant a larger pot is the time it takes between irrigations. If you need to water it daily in that solo cup, it's more than ready... maybe every 2 days.. as long as you do a good wet-dry cycle, that timing is sufficient.
You may want an intermediate step or two... 19gal is very likely too large for an autoflower even outside. The sun is a different animal, but it's still a vege-phase limited autoflower, so bigger pot after ~7 gallons probably isn't going to make a huge difference in autoflower growth outside... 19 gallons will remain too wet for long periods of time and likely cause rootzone issues.
I used some 7-gal pots outside testing some autoflowers. My backyard doesn't get enough light. They grow aboout 1M tall and were a bit lanky due to lower-end DLI. Even with more light per day, the 7gallon pots would have been plenty. Maine isn't a high dli region, either.. .but if you don't have trees or other obstacles blocking many hours of light, should be fine. 5-gallong might be enough... i doubt they grow more than 5' tall. 1' per gallon is a good generalization for sufficient volume.
Anyway, going from a solo cup to a 19gallon size is a bit crazy... it'll be really hard to water properly. The roots formed in a solo cup will never be ready for such a large pot. You'll have to do some weird watering practices to compensate for that context that will more than likely hinder the growth one way or another.