Congrats.
You should be good after 6 months with consistent payments (in the 680-720 range if you started with no credit history / a blank credit report). The secured card company you’re with will probably allow you to upgrade to a unsecured card, without the inquiry hit, or new account hit.
If possible, max out the card, and pay it off in full (a lump sum payment) at least two days before the billing cycle ends / closes (no less than 2 days, so the payment settles in time for the closing. You’ll clock-in a very small utilization on your credit report. The account balance gets pushed to the credit bureaus when your billing statement closes, and you’ll always close with a $0 or low balance (anything greater than 30% utilization at a closing is detrimental, less than 10% upon closing is optimal, but as low as 0% could be hurtful also, most recommend closing with 4-7% utilization)). That is a fast way for them to upgrade you. The reliable payments reflect trustworthiness, and the repeated hitting the limit reflects you need a higher limit / more room, and the lump sum reflects you can handle larger amounts of cash. Once or twice can be a fluke, but doing it all of the time for six months? Nah. Definitely shows consistency / reliability / methodology.
When I started building my credit I had no credit history at all, and hit 750 by the 12 month mark, 780 by the next year. But I went the AMEX authorized user, rather than the secured card route. After six months, Amex upgraded me to my own card, with a 3k limit ... since for the entire 6 months I maxed out my prior 1k limit and paid it off a few times per month (I stopped using cash and purely used my card to be able to manage that). Them seeing me reliably handle that amount, gave them the verification to give me three times what I proved I could handle (since less than 30% utilization is healthy, they tripled what I proved so I’d remain under 30%). — Anyway, 3 or 6 months is usually the “evaluation” period depending on the company. So if a credit increase is requested and granted, they evaluate your reliability at the higher limit for 6 months before they’ll allow you to increase the limit again. That’s the general rule of thumb.
So, 6 months, and you should be good to request an evaluation / upgrade if they haven’t given it to you automatically already. GL. =)