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I apped for SPG in Jan 2016 and got rejected. Applied again in Mar 2016 for that (and the Delta) and got both for 1k starting limit. I put hardcore spend on that SPG and went over the limit a twice charging SPG hotels and other purchases (thank goodness for the spend limit checking button). On the 62nd day, I asked for a CL and they bumped me to $2k in May. Fast forward 6 months (aka a few weeks ago), it's now at 6k.
I tried a CLI on my BCE in Apr 2015 immediately upon getting it and got rejected. It had a $500 starting limit, so I should have known better lol I just wait now-a-days. No rush for me.
If it helps: when I applied for the BCE this January, my starting limit was $5K. I called in upon receipt of the card tto activate, and at that point was able to request a CLI - I was bumped to $10K. My EX/EQ scores at the time were, between 740-760. So, definitely possibly to CLI immediately, but as always, YMMV. Happy increasing!