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Request when you’re ready and your credit file is at its best. No need to just do it on day 61 like the other poster said.
To put another echo in the chamber, you don't have to ask for it exactly at 61 days. I waited closer to a year when I felt my scores looked their best and I had solid usage of the card. Do you have BCE or BCP?
Nothing is a guaranteed lock but I personally would bet my Kobe Bryant rookie card on you getting the 61 day 3X CLI.
I cold apped for a BCE back in early October and I was approved for the same 2k limit. FICO Scores across the board were north of 730 but my AAoA was about a year. On day 57 after activating my card I impulsively requested the 3X increase and got it. I can tell you that I put a grand total of $51 on the card before I asked, obviously PIF. A school hoodie for the teenage son, and a damned nice one at that.
Again, in the wonderful world of lending there are no locks but from everything I’ve read on these boards it would be a definite eyebrow raiser if they didn’t give it to you. Best of luck.
I doubt having a balance, providing your not brand new to credit, will affect too much.