One determiner in the past of when a pilot may start training is seniority. Another is how staffed your current position and airplane is.

One huge hint to anyone training in IAH ....

Bring a jacket......

They put you in a classroom for a few days that is kept in the low 60's at best...

I didn't have one and I swear my concentration suffered from the onset of hypothermia...

^^ what he said.

Having any extended period off between indoc and systems will put you at a major advantage if you use the time wisely. Get all of the CBT's done. Also, start getting your flows covered and study the profiles. You can show up with none of that done and get through training, but you'd be a fool. And if you had any training issues, you'd get very little sympathy.

Showing up well prepared will pay dividends. The new-hires that had it GOOD were the ones that had a couple weeks off and were paired with upgrading captains.

How early after indoc (or during) will you be able to start the CBT process?

If I remember correctly it was towards the end of the second week... The Indoc instructors may tell you not to worry about starting them before aircraft training but when I showed up in IAH it was pretty much expected to have them done... I had followed the instruction of the Indoc people so it took some extra effort to get everything done. It's doable and didn't cause any problems but do yourself a favor and get them done early if you can.